W02K5H0P PRACIICE SERIES from Speticl Injeres, Model Books ' '' -: ) .1

. Hgrdenfng, Fempering & 13. Workshop Draw/ng 25. The Bockm rd Fowpldry '

bleot Trecfmenf Tubol Coin (j yerry Aspin 'Tubol Coin )4. A/la/tfng smo// workshop 2ù. Home Workshop é ?.?qfs & Tips ï '

2. Verticol Mfl/fng fn fhe Too/s Edited by v1c Smeed .

Home Worlshop gon Broy 2/ spjndyes k ;Arnold Throp 15 workholyfng in fhe l-afhe ' Horprit sondhu YX3. Screwcutting irl fhe l.oflne Tubol Coin 2g sfmp/e Worksbop Devfces IMadin Cleeve 1ù Ezectrlc Mofors ' x bol Coin Y . i4. roondrv ork for flae Amoteur 'Jim cox 2q. cAs for Model Engiaeers 1 Hcrold Hcll .'B T As in 17 Geors & Geor Cottiog o A o srown ' - '. erry P5.Mfl/ing Operutions fn the Lathe Ivan Law :jg

. wortshop yoterials . . ,.

Tu6(11 Coin 18 Bosfc Benchwork Alex weiss ' ''ù. Measuring & Markfng Mefo/s Les Oldridge 3I

. usefg/ workshop Too/s ' '

,.Ivan Law lq.sprfng Desfgn & Monufocfure ston Broy '

7. The Art of Welding Tubol Cain 32. gnfmof lII I-afhe Accessories . . . ' ''W.A.Vouse zg.Mefolworâ & Mcchinfng Bob Looder ' f

8. Sheef M efal Work Hfnfs & Tfps 33.MaI(fng Clocks . ' ' lR.E.Wakeford Ion Brodley stan Bray %' .

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. :9. Solderkng & Brozlng zl.Adiesives & Seolonts 24. l-athework - h Cornplete à i:i.

-.. . , r. j-Tubol Cain David Lommos Course i . '?

1p. scws & Sawl'ng zz.Workshop Electrics Horold Hall 1 * '' 'Rlon Brodley Alex Weiss 25. Mf/ffng - A Complefe ' @ '

1 1. Electroploting 23. Workshop Constructlon Course . .: J. Poyner Jim Forrest & Peter Jennings Horold Hall :

12. Drills, Tops & Dies 24. Electrlc Mofors in the 36. Photo-etcbingEjTubal Coin Home Workshop Brion King ze . .'

/ -.. iy ..uJim cox 37. Dividing . c ' . :.Id HoI I + ''' 4* 1 ' ' t' ) ./' ' )Horo u.. t . , ), . .) i. .''7

. ) -37. Dividing .-' , - e - : . * ,

. % . : * y.Faced with tlne prospect of machining a geor or gears for a proiect, mony model ' w- #, . , ''' , , . . .* '-

.. ù x % , .: . . .- . yengineers will be discouraged ond will turn elsewhere for their next model. This need notbe so, for the principles underlying geor cutting ond many other aspects of engineering '- . 'phere on accurate division of circles is required ore exploined in depth in this book. ( -xy - *

.+t'' )W . r. ! G . . k ;:.).'

It covers the subiect of Dividing, dealing with the many methods that can be adopted: : ' ' .4 z'.'r. . . . j. pï .ï . , . - )from simple opplications without specialised equipment to the use of o semi-universal *' : sss , t .. . a sysh VN .! .. sdividing head and a rotary table. The mathematical aspects of dividing are also covered . . lt ws . ç;.:o'v' ,- ..< .,s .ys . ) : l : ' . . o't e/.- . .b

ut ot a Ievel that will be understood easily by a model enqineer. Dividing eqoipment is a N !; k.!. .. x , < ,. , f ,,k .) .relatively expensive, so two fully-detailed designs are included ior dividing heads: o basic S .- / ,..j : . . v .. J .unit and the equivalent of a commercial semi-universol heod. .: ., . .

' '.. <,. yhis repotation as a mentor to tyro engineers t -s ' * -Author Horold Hall has established ; T

through the poges of Model Engineers' Workshop of which he was the editor for o j .. .. .ber of years ond through his other two books in fhis series, tathework - A Conwlete l - ' 'ZI. . :11 ')

nu m . . : :. kk., ;:: y ICourse and pllliog - A Complete Course. A s. . ;,: ,j. . 1k . ê . . I

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!1( POOle, oorset': BH15 2RG cbapter 1 9

England An introduction to oividing

' chapter 2 12The Machinery. Discusses the major items of equipment, Dividing heads, Rotary tables,irst published by Special lnterest Model Books Ltd. 2005i F lndexers

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Chapter 3 18i tified as the Author of this work has been chapterTwo to achieve the required. The right of Harpld Hall to be iden The Methods. Explains how to use the equipment in

.userdertesst a bv him in accordance with the Copyright, Designs and Patents Rights jt xso explains though how even complex dividing can be achieved using no otherht Act of 1988-. equipmentthanthat normallyfoundin the

-rorkshop, typicallythe Iathe and milling machine.I

! h ter 4 32' NO part Of this book may be reproduced in any form by print, C apAlI rights reserved.ithout written permission from the The Mathematics. W hiIst the tables provided with a dividing head, or those published inhotography, microfilm or any other means w? this book, will provide the information for most applications, occasionally recourse to

publisher. jculation may be necessary. This chapter explains the process, fortunately, theca

mathematics is not complex.

' @ Harold Hall 2005 Chapter 5 38k.Holes on a Pitch Circle Diameter (PCD) Explains the mathematics for placing holes on a! .

,PCD using a milling machine s X and Y table movements and their calibrated IeadscrewN 1.85486-238-3 dials. Also shows how using a computer spread sheet program can be used to IimitI 1SB

considerably the work involved.il) Chapter 6 50

Shop Made Simple Dividing Devices. Some simple devices that will enable dividingI - .specialinterestmodelbooks.co.uk activities without the need for a dividing head.

11 ited Chapter 1 58'l! Printed and bound in Malta, by Interprint Lim .l Shop Made Basic Dividing Head. A simple dividing head that is easy to construct, and for. most, will be adequate for alI the dividing tasks required in the workshop.

Chapter 8 716hOP Vade Full Function Dividinge ead. A dividing head that is more adaptable than a

ij Ommorcially available semi-universal head and providing a wider range Of divisions. It is1, nOt over complex to make and would be a very satisfying project to complete.I'1

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I,j az' cbapter 9' b its different Iength lines is made easy with

. shop Made uining Tool. Engraving a dial wit' Iining tool. lt is also an interesting project to construct.ii thisi!! 90 whilst in the home workshop, dividing is The book can therefore be Ioosely divided1 1c1 chapter t a frequent operation

, there are though into three sections.1 d their uses explained and listed. noprime Numbers. Prime numbers an many ways of carrying out the task. This is 1. The machinery

98 quite different to the major workshop 2. The methodschapter 11 ivities where round items will invariably 3'. The mathematics' iding head ratios and division plate hole numbers actj

. Tables. Tables for a wide range of div j-o tangular In addition to the explanations of therrence. be the domain of the lathe an chould make the need for calculation a rare occut are included. These s items

, that of the milling machine, with the equipmentand how it is used, the bookalso

''') shaper chipping in in a few cases. includes some designs for items that can$ '. o n t hl Vj ai dt j)i lg, , mh jOj jwj negvme ra' claj nn ebae nlaerrvi esdn tojtet tbjjeoms eajduesti ng tj vhoe twjj 00 rokos ohoosgsiatsryo l l rlaowt bj Jg ms 41 ui Rti drilling machine

. lt isthough, thewide range with some manufacturing tips wherehi hods that make the considered desirable.of accessories and met

I task a daunting One fOr many Workshop Dividing will almost certainly be a smallI owners. proportion of workshop activity, but without

' ln addition to choice of method, setting the required provisions, and understanding,it up correctly will often require recourse to some projects will either be impossible, very

. some mathematics. These, mathematically, di#icult or of a very inferior quality.are fortunately quite simple, but someunderstanding of their purpose is essential. Harold Hall January 2005

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. .' ' ( r r . ;( .' L; . /oj,ajyl'7 W hiIst the term dividing can be applied to . spanner to a turned component.r . a range of values, typically Iength, weight, The methods of achieving the division1

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.:1'' '- r% ' proportion of the activity Iimited to a small simple methods are notjust limited to lowerttz range of tasks, making gears Photo 1, numbers, in some applications, dials typi-..'. . dials, placing holes on a PCD (pitch circle cally, even higher numbers can be achieved

diameter) and producing squares and without any expense being incurred.1 f.

','. hexagons, typically for application of a For many years the predominant1. I :, ):t),'t- - ;. .-r. dr -;j ?; f$ 4, .t' .';r : 7

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: 1 t for only Iimited use and the expense as a re- ..! method in the home workshop, at easthe simple task, was to make attachments sult di#icult to justify, the latter may well be 4

. Making a dividing plate on a milling machine table using calculated X and Y co-/ for the lathe spindle to control angle of ro- the way to proceed. Because of this, de- ordinat

es.tation. Today, greater availability and re- signs fortwo shop made items are included

,I' duced price of modern accessories have in Chapters 7 and 8.' de this less necessary. There are still Using a rotary table Photo 3 is also ama( instances where it is wortb considering. possibility and whilst this item of equipmentI Carrying out some work on a component is primarily intended for the machining of' in the Iathe mounted chuck having just curved suiaces and slots and the Iike

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( been machined there, may be quicker than use for dividing is afso possible. .setting up the dividing head on the milling W hen placing holes on a PCD, work-machine and transferring the component ing out the X and Y co-ordinates of each

' ' to this. hole and using these to place the holes us-

lf dividing is to become an important ing the milling machine table dials as shownactivity then acquiring a semi-universal di- in Photo 4 can give a very accurate result.

' viding head, commercially made Photo 2 This can be padicularly useful if requiring a't.1 or made in the workshop, should be con- dividing plate for use on the dividing head@

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i he demarcation between these k,jlr)14 applications, even for the home workshop, however t' ied though in general terms, the is not always that clear, especially methods f.k is very var ,

methods can be reduced to just five. 2, 3 and 4.I' Using the lathe spindle. - '

Using a dividing head. 1 Using the Iathe spindle On the Iathe spindle. The Iatter may even 2, and erecting a detent from someUsing a rotary table. . ,ists of indexing the be in the chuck s backplate. The most convenient point, probably theUsing an indexer. This primarily conslocating into theteeth C'Ommon is to use the gear in the back gear changewheels quadrant, will overcome theDividing with no special equipment. spindle using a detentdisc that is mounted assembly that is rigidlyfitted to the spindle, Iimitation. Even where the lathe has aThe Iaqerwill be dealtwith when discussing of a gear or holes in a

frequently referred to as the bull wheel. One suitable bull wheel this arrangement willqï. .' well-known lathe manufacture does provide increase the number of possible divisions.'r ' '' '

' this facility and others may do also, it is Mounting the gear, or even a dividing plate,h :,: --'y ., though more common for the lathe owner is not difficult and a simple method for-,'

, to adapt the Iathe to provide this function. achieving this is illustrated in the section'g . jyjjjjj Photo 1 shows a typical shop made item. on shop made items in Chapter 6. A similar' C ti'.' tq One aspect of the Iathe that may make method for simpler numbers is to drill the. j ,I ) ,', r the method a non starter is the number of chuck back plate with a series of holes)

,l ? t ; ,, . .,, . .... .. . 'X teeth on the gear, if say this was 49 there around its periphery using a detentl

'J) .' t,., . : ) y , would be no useful divisions, only 7 being mounted offthe Iathe bed to Iocate in these.1 .

' . .t7 -t ; i 9- . , k . .?;? :r).:l'$ . . -# . available. The gear in the above example Alimitation of a1I of the above methodsttil ')). , ,:?) t ' -. , has 60 teeth and will provide 2, 3, 4, 5, 6, is that there is no facility to Iock the spindle11 - ' ))).f, k L, .. -. . ,(yy;()' kjjI . .- . .ij ;' ( kt, 10, 12. 15, 20, 30 and 60 divisions. If a in the set position, relying solely on the11 forked detent is used th is could be detent to hold it in place. Backlash in the. c :.

' '''!#' ' increased to include 8 24 40 and 120 also. detent assembly will permit some variation' ' .. , '

j 1 ,.. ' ,(' More about forked detents later. in the position set, and more impodant,r, 1.

i . .,j#77 '/. Indexing using If your lathe does not have a suitable movement during the machining operation.. . . . . . . . .. . , , ' .

'(j .. .)y).: ,t.. ''i ' ' the lathe's Bull btlll wheel then mounting a gear on the rear It is though quite adequate for many tasks1; g' ' wheel of the Iathe spindle, as illustrated in Photo as will be seen through the book.j . . ''jIi 1312$

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. This helps jy.oaie/t1 .. be firmly . ,, y .. ,- j,;. . . .jjj.jj .'q to minimise errors of position but more h' yjy

,- . . . j, t j ., $- ., gy , , .' -. impodantly permits quite heavy machining , tl ,' - ions to take place. yp(:)7)l, operatI èf- . 1--1 i 4:!), ,$/, 1EE,, d::,k y-r.j'l ; ( kr (! d q: -r.. ' )) ! 67 . r) i k-- è '. ' ' .l Rotation of the spindle is ac

,, fryjp,?,t . .-t ;.. , s j .jl using a worm and worm wheel such that ?7'r : y,jjlljqtttiyjpl .,,,-,.--- ., ., . -- ------ -,,.-- -,--,- --. ,-. --..-- ----,- --,,--.,- ----,- --.--- --.-. ------ -- -- ------

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. .the device and the input spindle fitted with 7 . (an arm and detent for locating in tbe ' 'dividing plate holes so that repetitive input .

2. Using a dividing head can be achieved precisely. Dividing plates ?yryyy,.,,,yyyy;yjyy;,y;yy,.,yy,,r , , , . ,This is the most complex and costly of the are available with a wide range of hole ''qlttdividing techniques covered in this book but numbers. By choosing the correct one andas would be expected the most versatile', with the 40:1 ratio the required division can 2a. Universal dividing head chain is set up for differing ratios, ratherPhoto 3 shows a typical example. As well be obtained by bypassing the appropriate Universal dividing heads, (the above being Iike the changewheels used on a lathe foras being used horizontally it can be set up numberof holesfor each division. However, known as semi-universal) are capable of a screw cuding.1

. vedically, Photo 4, or any angle in between. even with a wide range of dividing pfates much wider range of divisions, typically all The gear chain also has anotherIE The first point to note is that the rotating there wilt be many divisions that cannot be Values between 2 and 380 and many higher purpose and whilst too complex to be

achieved, particularly at the higher Values. This being achieved bythe addition discussed in detail it is worth noting fornumbers. At one time dividing plates were of a gear chain between the dividing head completeness. Ratherthan being betweenvery expensive but modern computer spindle and the dividing plate itself, but spindle and dividing plate, the gears are

' ?);)'' ''ttj,'ljltti'tc,tt'itl y?k').)tt controlled production methods enable the whilst still using tue Iimited number of set up between spindle and one end of the1 ,E')))y),)),.y;)-#.,yl.'â''.. #.)..,,;,t).tltt)j,tyt)y/jy)tj. punched sheet steel variety to be produced dividing plate values normally supplied. milling machine Ieadscrew resulting in the. (; ljiqtt . t,/j- ) , g '. :,rp..qj jji ryy yyjgjj4j-1k . ,. q.x jjeaply. 'rhe drive from the manual crank output from the dividing head rotating ashl ; 1) very c

Mounting the workpiece onto the handle to the dividing head spindle is still the machine table is traversed. By this

i' dividing head follows very closely that of Via the worm and worm wheel. However, a method helical flutes can be cut. Should0 j) in from the rear end of the head this be of interest, search outother reading' : the Iathe having the facility for fitting a gear c at

spindle is then arranged to rotate the on the subject.faceplate or chuck, Also a centre can be'il ' ith a tailstock, either supplied dividing plate itself by a small amount. This. fitted and w' ,' ) or available as an accessory, between has the effect of marginally altering the 3. Using a Rotary table

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);. L' tres work can be carried out. rotation of the crank handle for a given The demarcation between a dividing headi ,, . . y#yjttyltlt-,st),yj ce n< . . t y,,y.tt number of holes. The outcome of this is and the rotary table is rather blurred bothï '. - :*W .

.1V, ''ljj; # A semi universal head can also be that divisions not obtainable with the semi- having common features. The major one:

f : kk trytr, tjnjversaj head can be Set U;. Yhe goar being 60th have a Worm and Worm Wheel': iqf' lljtplpqr. .,,#r ?-' '

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.. su/aces and curved slots. Placing holes Holne workshop made items - 'J' ' --'h ' ' ' ' 'K ' :'- - tv##)''tpij.kjytjy.y,;yj,).,jjjr.y.jytt,k((k(.. ,ç. . . :#, .. r (j .

, ,, 1 ' ,,t,t-t''k.(tkt.y y,,nt ,, on a pcD is also practicable for lower The com ments above rega rding ' r.ï?.$,t))j)?ylt'j

yqjjth;j'(jyy:: $$442.,: . . . .., . , j jj j! :t;.. numbers where high precision is not dividing heads and Indexers are made ' 't$f1.'/,y4?,l)t

yt ''''',..,#,;)

,. requireu. lt would though be questionable primarily with commercially available items ' % Yl:/J')'1'l,)j j for a large number of holes on a PCD when in mind. They do though in many cases also

. 'jyjttjjjjy,.. . . j' ' .. .t making a dividing plate or for producing a apply to items made in the home workshop. Yjjjt(ltlttly(:.1 .. è . yjjs

yyyjyygy .jjyj yyy jjjyyjt. j;;tjyty. gear. Most will also be suitable for vertical However, many home workshop owners do ,ké ';/ ty, .7/.774/ ti

ng. Also available as an extra in find much simpler designs adequate for ' j,/' *ù.g,l.)1'ë)j1,@.li')#ë0:,:i'. ,,t moun . ,'?'V some cases is a dividing psate mounting their needs

, that in photo 7 being an )r't)7'@C ' ''tt ' ùt) arrangement as seen in photo 6. w ith this example. w hilst for this t:e title ''Indexer''

jij,nbibi,q' ; 1'''. k ? . s . ... ... ' ''. available there is little difference between would be more appropriate, such devices .7 7i'tt'.'t;')''lt '% . ' '' ' '' ''. sgj. . l ''u s a dividing head and a rotary tabie, other are invariably known as dividing heads

. 47'lE.t't- .t-ètxt than the provision forworkpiece mounting. Designs for that shown in Photo 7 and ai , 'lj 1,14, y

t,.),'jiy.r jf the budget will stretch to it and you much more adaptable head are included. p)())@ /. -t-.:t.yyy- . ,

i . .

.'#,,)):y,.!),l)i,,)).(.;,),. purchase b0th a dividing head and a rotary in chapters 7 and 8. In addition, many ;i,.

ii . t7. llll'l,#)',yttti , ,)),).t, tabie from the same manufacturer, it is likely supp.liers to the home workshop have

,' . J' ê)y, h4,).. 'jtllii ïjrat t) è.ly,yy,.,tjytyy:y thatthe dividing plate assemblyon the head designs and kits of padsfor making dividing!

. '. )f:t't.),$

.tt-Tj.,k)?è:t)y).tj)i)t.pyf),t,t4:.;'!))rt,,,t . ttjy wjjj ajso fit the rotary table. Its tailstock is heads and rotary tables.

. .

- .-s,,. - ., . y- . ,.'-rjyj) q;rjyj ,. - ..y)j. . j ...).b j(. yj.j,-j,y;,rk y,.y,j.yytr-y,y tqltqj:j yy , yypy. y-

.

.,#.( jy. r). . . . r.- )-- y.. .)%'t,#'? .k'$. 7 .. . ;:.jtj,;,,,-:ë),).r),j,),,! ,. . , jso Iikely to be usable, as these are .,. . kz . .,g, . = :6 a

I 6. Commercial rotary lab/e,s onen hale a adjustable for height, see Photo 2 Chapter 5. Dividing with no special y$,ç )dividing plate assembly available a.g an 1 equjpment E ,5)t'11' (E'' . .... ..y , ,. # ( lp (jqy)- ;-,)@. . . ..BCCBSSOW '

ùDividing with no, orvery Iittle, additional t . '.',)jy y, y,between the manual input and the rotation 4. Using an indexer equipment can often be carried out and is Ci''V1JliVt , ,' .4:?t;t;: kp't 4ir );k - 7 y k - -yy tjty- -k jyj ,.,,j y jt yytj y $

,y- . ,..,.. -yy tj, yy- -y .y.

... t- .. . t. y.

.

g . ë )- . .,

.

.hough there would This is a very simple form of dividing head worth considering even if the workshop is ')1/t/''1)l 4#./ .:i,1, . t (,j t. d::)l jlr 1l: 1,.1 4E!,, lk/qklr 4::)1 1,. !< j::)k i 1E5l, 4::: 425), , 1t: . tyjy j;gy. , ,,. ,,, . . jjjjjjyyy.yjj j. yyyzyjyj y y yyjyy.yy y,ayyzs

jyyyyyy

syayyy,

.yy - , ,ayj - .y.. . -q

.

. .

: appear to be more variation in the ratio's having a rotating work holding device that fuqly equipped with dividing facilities. It may ttt). svtltt--ylsitt-il'1/'z''' j,1.'('' . !.?. évèjt.e'ljr?s4tt,' 'ttt ly,.yjxzt,ry. .. ,,j, ,

1. ava il a ble , 4 0 ! 60 a n d 90 : 1 al I bei n g is rotated directly by hand, there being no be expected that such inethods are Iimited '<-r''!'.*'-î'rl*.,,'a1'.:- 7)#0,:,p.'/l)''J'?-l..ll.7,.'i1.#:.,#,f:s'.,c 'ù'v 'k-rp ,)s. , ,common. The major differonces are in the Worm and WormWheel. Angle of rotation for to the simpler numbers, 3, 4, 6, etc. but as z

. m basic home made dividing headI

rovision fOr Work holding and in most each division is either set by reference to a will be seen in the next Chapter much more$ 13: cases the method Of determining the input 360deg. calibration round the edge Of the complex numbers

are possible, even those'' vajue. For work holding, rather than having table or by the use of a number of holes not available with a commercial dividingl'

facilities for either a faceplate or chuck, the round the table, maybe 24, into which a head.1

f monl rotary table has a T slotted round table, detent Iocates giving a range o com1 Rhoto 5. lnput to the worm is determined divisions.llb by reference to a calibrated dial rather like lndexers are normalsy fitted with onlyi'

dials on a Iathe or one method of work holding, being either athat of the Ieadscrewmilling machine. In dividing applicationsthis three-jaw chuck or collets. This severely

. only works well if the required input falls limits the tasks they can perform. Some are 'exactly on a calibration, otherwise errors also suitablefor horizontal mounting thoughwill result. of course they could be used with a

! Rotary tables have therefore only substantial angle plate. Commercial items'i limited use where dividing is required

, their are not really appropriate for the average'1'$ main use being for machining curved home workshop.11i 16

17'j

11 t 'b' 1t

&'' 'j . . '

i I

1,. p. a e duaystub. mandre/ for, i1 motlnting bah gearI d dja/.an yj: . . . .y ;' ! .' j '1

et set

'

,.i t-. . , k'; '.4: u

. ) .1 $ : ,j l

. . . ,

li Equipment. because either a dividing head or t'ae y,' ..i using Minim um oatoe ,y? ,.division required is not available or1 Having dealt with the equipment required ; ;::.! iding project is simple and more easily set up .,i,(;j,, tchapter 2, it also mentioned that div . y .,; in

her method. , ,., ,;;j?ith little or no using some ot ,can often be achieved w

1' ecial equipment. W hilst using a dividingsp her Using the lathe spindle three jaw chuck. In this case, placing a third space would give the required result.d will in most cases be the ideal, othea f this would be when needing piece of packing between the bed of the Also, by careful choice of a thin piece offten used. The reasons for Typical 0

equipment is o item in the Iathe and each chuck jaw in turn would be packing to place below the bar, or a slightlyften be to make three divisions on anthis can be varied, but will most o accurate enough for most applications and longer second bar, a 50 t00th gear couldr. .r ,., . ..-, ' . : cedainly much quicker than setting up a be used to calibrate a 100 division dial.' s ;;y,'''L''(%'1.,F111î3L(''2'%' t dividing head. Do not fall into the trap of Another simple idea and only Iimited. f ) #tq ) j ).j-.(é F,.( i i... .. !I1' .')4-)'.ttt j,;,i ,sttajtjyy,,liks-.- .. thinking thatjust placing the packing under in the number of divisions by a practicali )7'itv'

.'1' t,/.?C?,)t,t . oejaw in the rear position will give you six maximum, is towrap around the back plate,! t,-r-' (,,', ).. ',?..', y, djvjsions, this will only work if the height of or face plate periphery, a strip of paper' i/' ..t (.' ,!. F ..:.:, . ,4,,:4-3. . . . ,t ' 7 )' I7;k.. ' , .:*1-* -z') ,,,,, .,.v . x. the packing is exactly centre height minus suitably marked with the divisions required.

. , ......., half the jaw thickness. This may seem a simple idea butthe spaceI' An extension to this idea having the between each marking, when in the flat, is', advantage of providing a wide range of Iikely to be a complex value. Say with al divisions, is to include a gearwheel into the 100mm diameter backplate the'j set up and use this in a similar way, Photo circumference would be 314.1593mm .' 1 Using a weight on the end of a piece of Dividing this into any number would resultI .t string attached to the chuck, as seen, will in a valuethatwould bedimculttoworkwith,' keep the short Iencth of bar in place whilst fortunately

, there is a simple way out of the, . theoperation of c Jtting a dial is carried out. problem. ' .' 80th earand dial being madeare mounted w rap your strip of paper, a Iittle on theg1 '

1 . us in g a g e a r o n a Opl oat od la.

i otaf Pcllltslb ymoa; dd )e 'n l't nloel' ti on l tl negc l iudcl Ca IdS 1 Ya rel UUIRI yd cl to t I Oroli Pgle l'J o tlfh! '

t 'stub mandrel to cu use every t00th space, if you required 15 with a sharp knife at the overlap, you will'i.,,,,tty a dial. divisions, a 4s t00th gear stopped at every now have your 314.1593.m strip of paper,i e .

t 1 9i 1 8I21

y'j ' '.t,

. j jf- .1 hI II I I II j IIi' d' ided apfr ' '' '''''' ' ''''''''' '*' '''' -. -.?. A v p ,, ,. , , ,I I . . y. . . . .y ..my.. 'III ! ! Stflp dCO&r?d . , ? e'FL$, , - àir- .11.1 ' To 2E avlnEa / ï ? t chuck's back plate k, r .û,t.tt .. v .,I t pg E2 $/4 q (:;.,.s... . : .j I ' j j . s . . , yr ; . ; .) . .. .. . .11 for calibratlng a

.'. , .

I I I Y . lt y1 I ENCIH IHAI CAN / /î l CII*I i'S ''C''D **S.V '':'iF7U ':'1t'1I LINE OF A L . , :III I EAslky gE alyj()Eg lNTo THE / / î $ practical approach , . ,... ,... .,.,,, .I 11 oNs FEQUIRED

. / / ! l r '..' . >''*' '11 j NLS:8E, oF nlvlsl /.? ssk. ,k. . ., . . .,,... .I : to t e$tI I t j / t

I 11 1 / / ï ï

'

-

11 t ,. I / ï ! q .-. . . , .

111 AIGHT EDGE lS SET S0 THAT / f l y , . . ', ''-' / ''bV 's'rq

11 11 i TsE EDGE oF- IHE SQtJA'RE LINES I ., ... . ' 'l UAF'C ON THE / / h . ' '' ''

. I 11 tJ? AI-IH IHE FINAL y1 1 * ANi) 1HE EN9 ''ï'' OF IBE II'EM / hLINE y / yI'I I gElNc ajvlns!l l / l .'i1 $: / 1 ïh /

/ y y -11.11 (IikIUCFIISMAN'S FQtJARE ïI î' ! I i h ! -I / I ! 7'I l I / ï .,....t.f,,.'..' jl 11 h . . : .. F '''r/q11 , t - . ....- ? . . p'#I (1 I T8E ZZAUGHTSkAN S SQUAFE IS l ,, . '' 'fu jt IMiSIONS 0% TIIE UNiz t ï . ''''* 1 f.; .t S'IEFPE: ALZNG JHE E) ,ijjj;);)4 s11 I IRANSFELIkikING THE: To THE IIE: SEING DIVIOED. * ' .. )) j,I , .E :)k. j) )j jI j . , .( k j; 4 tjly y, j. . k yj (jj . . ., r . . , .I j .. .

I I I I.1 l Fix this down on a piece of paper and on Iong enough, cut two wider strips, peel back' I Ii I

.1 x jawprR this draw a Iine at an angle to the strip of a shod Iength of the backing paper on one11 11 SHEET OF PLAI

$hlj VZIH-O-D - A paper and starting from one end of it. For and join together. To ensure the required '-lll j example, say you wanted 19 divisions mark strip is straight it can then be trimmed toI

.I I the Iine at 285mm (19 x 15) and mark this the width required. Thoroughly clean theIl; Ek Tc gE ()IvlzEp ohTo A SHEET off at 15mm increments. Using a straight faceplate or chuck's backplate edge toLAY IT1I1 OF UNED PAPEF ANp AI AN ANGLE SucH ,pAcEs edge and a draughtsman s square as ensure adhesion. The process in SK1 is a1111 THAT 1! SPANS lHE NUQBER 0F S$$! $ uuàL To THE NUkEER oF nivlsloNs illustrated in sK1A, transfer the divisions rare occurrence in theworkshopfordividing1

REQCIFEZ to the strip of paper that will now be length.1II tely divided, If you iaave a large sheet A11 the methods above have one majorI accuraI I11 I11 jII of Iined or graph paper, then an alternative, problem, there is no method of securelyI

I 11 and probably easier method is illustrated Iocking the spindle. W ith only a Iittie careI.1 I in SKIB. Fix the strip to the chuck and use this should not present a problem for thet $ :111.111 this to achieve the required result. photo 3 tasks shown being undedaken. For moreIlil shows a dial being cut in this way

. As an arduous tasks though, such as machining1111 IIIiII1! afterthought I realised I could have marked a hexagon on a turned item, it would be aI ' I

I 11 I tbe strip with the positions for the Ionger non starter. Because of this, even though.111 Iines

. the system can easily cope with anyI I1. l APER A ideal paper to use is an A4 sheet of number it would not be suitable for cuttingI 1. SHEET oq- LINED P n

I I I V ET H-Q D- 2. 'adhesive paper as used in photocopiers or that gear for which you do not have aI

II . computer printers when making Iarge suitable dividing plate, there is though a' I II

,sK1 Dividing length adhesive Iabel s and the like. If this is not simple way out.I1

i21

201

. I

I ' jtj' I ''

.1 I I I I '.. I ''' . '.cw - . c I j

, jjljlf l

'

f

I ' II I11 I '1f' I l ?y.y jp pjate. The positions Can bo established7??IIr ' j) mounted 'q ryi)

, 'è ,>))r,I J 1 - - using an automatic centre punc . ,./1 f (

- , . ; it . .. .I '. , t.. j on the top sliue, or, if available, a small . . .,,,,,.. ) ., , .r,jy), h jj,,., ,, ,.7 '7 -- - '' '' drilling spindle as in photo 4, 'rhis process .41.71:4' !,j ''''k' ......';kk :itzu''''''''. - t.''''#,,11 ' l k ; cs f ,J w - ' ' . . . . . i)j k' . .. ' ' '$f - . should make a dividing plate accurate .. 'W .

. ) . 'III 1 , . . g )j.I . '.t r . . : ,) . ! ly . - k r;jjl ,'' . g mi enough for most applications. However, if :r <

o x . .r j7,,'','qt' #. . '

(-) ( . . . k# '.- ; < ( sj'r ' .t t11 (. t,yltttx- :- ., ,,,. , eventualty used via a worm/worm w ee , . , . , .)qI ,-).i. . . t4-F. ps . . . . . ji. rk . . . - h. .. .. - ; . . . ,

II: ' - :î . rath e r tha n d i rect, the i m p rovem e nt i n l'%t4 ktl, , )j'y ' .. '' ë( ' : ikthtaijJ 1 ' J .j . .à l > j t jjyjj jj g. ), ; ygj ky)y y jyy '' jy

ï

,

'y . y .:...t , . . j .

. ..

. .11 ff t - - accuracy this provides, as described in i .I ).' '' . .....t.

' '' t! (ll ?;' i) j) : . - r 4

- . . ' '

j- ds - .11 j C - Chapter4, would certainly make it adequate. ' h r , ( . . . .,tij .. k l//'J/I f ' - . lncidentally, the bar against which the E . ; t 'I ?. . . .y . .11.1 Y. faceplate markings are set uses the same ,' ' r, i, ) y,''1 ' ?''' two fixings as that for the bull wheel detent '' '''''' ' ''''p/ ; ). . . j

I f p . T''.), . ;..y... l . . y) 4 .' .. .I t.,. seen in Photo 1 in the Chapter 2. * : y

IJIP ' s..k rr,)) s ho u Id vo u be m a k i n g a s m a l l .

'

lfl - . y*#'/ è$., ;. . .. ' / stationa ry stea m en gi ne ( Ph oto 5) the . .>kkyv,,. ... t 1) k7;, . ' . ,n'.jII) ,,,1 j . 5. Fhe statlonary sleam ettglhe requires 5 E tyt. . jk . . , . ç.j,j.) jlI l j!

, cylinder end flange requires 5 holes on a ,.

1 I , ? .s T , , , . ! : h o /g s o n a 8 C D m aw : z

:

/Ig J I PCD. Positioning trlese prîor to removlng ' r . / ul%% post reqtpres jhal a hexagon /'s. I 4. Making a division plate using a divided tjl e f ja n g e f rom th e I at h e afte r i n i t i a l machined. ,lII l , .I .. I naner strio and dnlbna spindle. mraositain/a nfanla so cl/ane. However l chose V '. 11/1 ) '- r' r' - --w-'-'-k' - -'- -- --- ' , wjneel to set the divisions, photo 6.' flë Mount a disc onto the face plate and to make a small drilling jig (seen in Photo sET LEVILIlI I ing a suitably divided paper strip round 5) for the purpose and using an automatic , The following would have been anus71 / ' i hery will enable tlne centre punch mounted on the top slide to alternative approach to indexing the fiveJ the faceplate s per p

s:r o (jjvfsions. Five holes on a Pco requires a! ,l disc to be marked Out for making a dividing mark Out the positions and the lathe s bull 48 gESqEESj j .. yojsjjos oy yryyoyy. yojaoos osoyj aosjyjoyy.I l ' :4 yjp : y .i t)é, A) 'Fhis Can easily be achieved using the jawsI g

,,y yty .. ) jf .,j.s. . . y , y.j oj a tjroo-jaw chuck and a combi nation-I I j I ..) . --. . E. .. . - h. ' . . . . . , . .. j.. . ..

j f j s . .y y . sgtjare protractor aS illtlstrated in S K2 AI .. ' y. t , , SgT JO .j r j, ,) ,, ., ))j y j;. r. 2j g jryggg g y;j astjc ba n d wra pped a rOU nd th e Ch u ckI I . .. p . . .. '' . . ,1... ç (jy;ï t)ëgt ... .. ,@)ipj'(j /!.î ' . ,/,fj,, , .,. . -? ))). .,.),t,. t and weigjlted, would provide some frictiool

j'j2. . . , ,y, y ,-,'),,, .

. .,, , .

y ï' . lj,jtj'jxii''vvt) '.y')#yJ, --.,yj .jt,t,,

,.yty,yy. yy,.

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,

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sto sateidmsteytstionrgetajonadjyyhoooldu iyyngytoyjssistiyo no. r-l-ahrtysJp , E k , . . . . . ) , .; ; :Ij I Ij I j ' . )ààLfb3, ' $' ;:.. .j ; . f3j.'..t yjy.: . j .y ' .t ' ,yt#) s?' yjjjjrf . x Jv jj yyjjyl . . , ljj!@ f ' ic'

t '' 11* 11' i %' Q I ll:il$'? : ll''1t q lliibCY'' jjjjljij' ' i'Fflj;i 'f' i

'

1C$' ''61If 11 ; .', , ,u ,. ... ., 'tttltjay-

.,;t '. ytjlrt(vjt, . . ,w,tj- ;, y . o xu a uto ceptre

yjy ytj y;n u m be r of d ivis io n s , its use is tho u g h o n IyJJJ - / . ..

.. . . r .fjjfsl , ... t

, ' ' ' ...,.

,;' . ,y ... ,j, , . y ou tye toy 24 jggyggg ,. . racticable for low numbers

, even here it's11 j J j I .. . . r;. jh,. t7, )ùf) -Ti))) ftb .. . . - - , ' ' . ' jt:sh 12./' /.'? t:;tfIII''I . ' (v , . w '' ''....k''ljyj '/q . . slide is being used B Ot a f i rSt ch o i ce meth od b ut wo rt ht /rI , ,, . ' . r), . ') . .. ). considering in some cases. Using the four-. 11 II, I . . , ,* ,,) ). ;; . ,,, , to mark the five *I I III T . u EE); ''''-')% ?)t,t.yyj.''.

'' : . .. . yosigons for the àyy )(; -

jpoW Chblck Would be an advantage for some'

'

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(jj(:. iy .

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y.kë' 1/3, ' , .t jjj umbers

.I '' I I '': 'r '' ))1)i-;t;/;?)j?-,j.jyy,yyy. ..' t'), lt '' $) fé J ty/tj/) )r' lj.' ;êè( /. t:;l :j?'- kf /F j,'i' t::/r d!s;, j'- /$'? dEEl i!rih 4::4f kl. 11: (2t (E (:; @k! E: E2 :5;' I '!1/t@ ;.)( ''.r' . .. . ?. ,;j .. - . . ' #j(j î tl f)y))). ; . . . . , . . .I I r ))/ ; ., ,?, . j:, .,) ,j4 .,, yj dnnirtg jig. The yup .. o jjje mjjjjng mach i ne

.j r . u; j ;y g, . . y. y j ).y cou gojjyg ..+ ;.sJ j? yy. W Qe's ' .. ' 3:11/ /' The smal 1 ost seen i n P hoto 7 has aI I . ,' . . . :... ) . . r îi: . .

' li 1:),,./,.,' ,' , .., ., , o the angle between) l p' '

.,:.. t '# ' ':J'%. : '

, djvjyons.. .Q c o o a.a ol:a a r x ;..:.. :. . w mSXRZRRPC hOXa9Ol3 that WaS machined aS

. , y,jo .)pw . 'v,):h().:... w nm w j =a tj n u u u j v jo jous ouown in Photo 8 . A temporary hexagon

2223J JI

f '

/l ) 11 '

I 9.. ',tL . k

headed screw in the bottom is used to setit up for each facet as shown in Photo 9.W hi1st this is not that precise, it is, if carriedout with care, more than adequate for thepurpose. Aiternativeiy, it could be set usinga square off the table surface setting oneface of the screw head upright.

Using a ruie and a square on the same

9. Setting eachfacet of thehexagon headscrew Ievelusing

by eyea steel rule.

24

workpiece would enable twelve divisionsand if only every third position was used asquare can be machined using a hex headscrew.

The above illustrate just wbat can bedone using the bare minimum of equipment,no doubt some readers will know of, or beable to devise, other methods.

.1/ (!;' t:l;l ka / I'b kr'a ttl'l-î (:)! k!p . . s:r r. .' '.

'- ' .'L. . .:t. -.,. ..k., -

'

h-' .. '

, ''::îàJ'q. . .'.; . ; '..rotarptable table ' x,. . ,

. r.yyk..)with 360 divisions. .

' : : :,. ., '''k u jj' . .. )j q . r, tt aoividinq head ' > q. ' ' ' '' '':s,+' -'. ' .L . s' i 7

' d i'S lhal 1 '''belng use kj ,#z o :. . . . .y'''- l'di ''Lbb k,b kiliq '' , . .)., ,.. . . ...t'-)'Jin Chapter 8. jwox#kyk; v . . ,, ,yj: . #tA jj 19 j; . . '.' .1*. ' # . ,Z k jlq. j, u' l## 1))é :1 : a. y y ,

?ij)1 idi dlp !I' ' '' ï .. ' . ' .. , t1j.

Cjj;kjk:.'jjj1!q y.. jyjdlh . t j jg j.';.

.

a. . ...

y .j5 ' 4 i'.. yjl:.! î (t' ' 6'' . .. . j yy . y

y . .

jjjj(. ..yt . jj j yq. . . j . . j s) . ..

' .:fb /1.kj'14 y c . i ; . , j;.... , jt..k , . . . - ...

. .i ik .ij . lj:y qdp .i rràk ;)'E .. . ,y k ,.. .. #p qcsr. ,. s ); ( .. g ...,1r !#%,j; dd . ,, ' S.ljjt..j ph,s,. . . ,4 llik . : stj .k##' # . '. .'# o ..

W t' : ùl ) j : .j - . ' 1 rt l $j. ; à' 2 '. t.k .

j .' )

Using a dividing head.Having determined which dividing plate

to use and the number of holes to betraversed for each division (this to bedescribed in Chapter 4) there is not muchleft to the exercise other than mounting theworkpiece and carrying out the requiredmachining operations. Anticipating that

r ' q'.: ' '%qj'' '' ' .

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.A , ' ' ... . !L. .k4. '- . . . u.1 1 . Calibrating a ' '.. ,

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. 4dJ'a/ whl'/sl held ona stub mandrel.

The (//t//t$r?g head y'tilgkgyyijyy.yvyyjj

vjjjjy ., ..,wè /() ê t ' ' .being used is that .(!t g , . .,t; . 2 .' Cha ter 7 '' C- 'iz '7ll? p . j. : .. .4, .

25

anyone arriving at this point in workshopactivity will already have gained the skiîlso f m o u n t I n g a n d m a c h i n i n g , t h e re i stherefore Iittle that needs to be stated. I amthough including a few photographs asexa m ples .

Mounting the workpiece will normailybe straightforward following ciosely similar

.. tp. vachining3). t ..'g. Spbnes Or1 a

9 ' jl '- .lE tT),' between centres

, , J shaft+ j qî j ..,' , e r .): yr . .. e r' +

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operations on the Iathe. Frequently it willbe to use the three or four jaw chuck eitherholding the part itself, Photo 10 or using astub mandrel as in Photo 11. ln many casesthe component being machined wifl havepreviously been turned on the lathe and tomaintain concentricity it will be preferable

to move it to the dividing head withoutremoving the workpiece from the chuck. lfa part has an irregular shape or is too bargefor the chuck the faceplate will have to bebrought into use as it would on the Iathe.

M o u n t i n g t h e wo rk p i e c e b e twe e ncentres is another method of work holding

. . :?, .:.z(.jt yj .; g ;) y y ..( #yj : () yjyjyjryjyjjyy. . . u;:. . a .y ytyyj yyj. . ' y y

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, .. . ' t gr ., - .j. . S 's ..

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26

nd is obviously used where the part to beamachined is too long for either the chuckr the faceplate. Photo 12 shows a Iongohaft having splines machined into one end.sw hilst appearing to follow exactly thesituation when mounting between centreson the Iathe there is one importantdifference.

ln the case of the lathe, the Iathe carrier(sometimes known as a lathe dog) mountedon the component wist be driven by thedriving peg mounted on the catchplate. Thecarrier and peg will often be held togetherwith a Ioop or two of string orwire but reiyingIargely on the machining force to keep themin contact. This will fnOt 3ufflce When uSil)9the set-up with a dividing head as the 34 c/ose up of dividing plate fingers

.machining will not necessarily keep the 'driver and driven together. Because of this traversing 14O holes, or in other terms, twothe driver di#ers from the Iathe catchplate turns plus 42 hoies per division . Thewith driving peg and enables the driver and mathematics of this being 40 x 49/14 = 140.driven to be rigidly coupied, Photo 13 It will be obvious that whilst two turns wilishows the method. See also Photo 2 ir be easy, counting the additional 42 holesChapter 1 for an iilustration of the dividing at each division will be prone to error.head's driver. Lathe carriers with bent arms Because of this, dividing heads areare available but the position of the arm fitted with adjustable fingers, Photo 14,would depend on the diameter of the which are set to the number of holesworkpiece. Unfortunately, I have not found between one division and the next. Thesea commercial carrier that overcomes this hold their angular setting whiist still enablingproblem, though they may be around. I them to be rotated as a pair between eachhave therefore developed my own design division. The construction has some inbuiltSeen in the photograph and which features friction that enables the fingers to bein Chapter 6. rotated as a pair whilst being sufficient to

Having arrived at the point where the ensure they remain in position during eachComponent is ready to be machined and machining operation. Mostly, fingers andarmed with the correct dividing plate and input rotate in the same direction but duethe number of holes to be traversed, to an upper limit to the number of holesmachining can commence. Taking as an that the finger can span, typically aroundexample the need for 14 divisions using a 75% of the number of holes in the ring, fordividing head having a 40:1 worm/worm Iarger numbers of holes they rotate inWheel ratio. Typically, this will use a dividing opposite directions. SK3 should make thePlate having 49 holes and be achieved by situation clear.

27

1 5 Machining w#/? a vertical dividlhghead will result in the cutter allempl/lpg tounscrew the chuck. Very Iight cuts aretherefor essential.

If using a shop made dividing head witha gear to replace the dividing plate, thenthe facility of adjustable fingers to determineeach division is not Iikeiy to be included.This statement based on the designs 1 haveseen, including those in this book. However,I can see no reason why such a facilitycannot be built into such designs. W ithoutthis it will be a case of counting the numberof teeth traversed with considerable care.lt is frequently the case though that thedivision is achieved with one revotution ofthe gear, such as every third t00th when

Using the rotary table.If you have a fully equipped rotary table,that is with dividing plates and tailstock,then the above explanations will largelya p p I y w it h o n 1 y so m e s m a I l c h a n g e sregarding workpiece mounting.

If however, as is most îikely, you havejust the basic rotary table you will be facedwith setting the divisions by using themicrometer dials at the hand wheel.Consider using a table with a 60:1 ratioworm/worm wheel and 60 divisions on thedial giving O.ldeg. rotation per division. Ifwe now consider, as above, a requirementfor 14 divisions this will require and output

using a 45 t00th gear for 15 divisions. W heretbis is the case the gear can be markedappropriately prior to fitting it onto thedividing head. A coloured chinagraph pencilis excellent for this. The bull wheel in Photo6 has been marked in this way and may bevisible if the final printing permits it.

H a v î n g s a i d t h a t i n t e r m s o f t h emachining operation there is no di#erencebetween normal milling operations andthose using a dividing head, there is onepotential disaster area. Photo 15 shows ah a n d w h e e I b e i n g m a d e b y m a c h i n i n gn o t c h e s a r o u n d i ts e d g e . C a r e f u Iobservation of the set-up reveals that thecutting action will be attempting to unscrewthe chuck from its mcunting. lt is essentiaftherefore that the chuck is very firmlyscrewed on and that only very Iight cuts aretaken. Should the chuck become free, thenthere wilf certainly be a spoiled componentand probably a broken cutter also. Do beaware of this and take great care whenworking in the verticai mode. It can alsooccur in the horizontal mode js somespecialised situations.

' ; ; 1i ï' '. .. $,.q.hexagon for a Iarge .'

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16. Machining a

of 360/14 degrees per division, that is25.7143 degrees. This equates to 257. 143divisions, or 4 turns plus 17 and a Iittle bit(0.143) divisions, it is the little bit that is theproblem, lf the task is to place 14 holes on

a PCD for bolting two flanges together thena little clearance in the bolt holes shouldmake the approach possibse. Do not thoughsimplify the figure to 25.7 degrees as theerror of 0.0143 will accumulate over the 14

INPUT ARV IOVUQENT1 s 1 j .SK3 USING o ooo z'' ooo.o 2'Xi ooo.oooso oo o Xjg ooTH E D IVI D - ooO o

J,, ooo Oo â,, ooo

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o o oo oo O oo Oo ooOooooo Oooooo FSNGE? ooooo/

k ()v'g g g N T/.st / !s1 1s1'J1i)n d ?n d 2, doo n Oon oo OooJr *0 r () * 5r **()() O O

O(7 O OO O O O O0 O . O O Ollh Aqyj () #1n (7 4fh z#r--xx (JOo J oo Oo oo ) ooo o o o o oo o o o o oo o o o o oo o o o o oo oo oo oo oo ooOooooo ooooo ooooo

/1 is normal for dividing fingers and the input arm to move in the same direction. Hokvev'el:d&& to a upper Iimit that the dividing fingers can span

, around 75% of the maximum, for/oNer spans rotation of the fingers l's opposite to that of the input arrn as shown aöok

'e.

28 29

.- . - . . - - ; kj

30

1 7. Attempting the task in photo 16 butusing a dividlhg head in the vertical moderequires a Iot of head room. It is though anon slarlec see comment fOr Photo 15.1 8. A/l'gr//'r?g centres in preparation forpositioning workpiece.

d i v i s i o n s m a k i n g t h e 1 a s t h a v e a nappreciable error. Do though work out afigure for each division, say 257. 143,514.286, 771 .429, etc.

From this, work out the turns anddivisions, 1st div, 4 turns + 1 7. 143, 2nd div,8 turns + 34.286, 3rd div, 1 2 turns + 51 .429,etc. Whi1st this is possible, it has to beasked is it practicable having to carefullyset tlp each position? For the examplegiven, probably just, but whether you wishto count and set up each position in thisway will be a personal choice. If gears areto be cut or a greater number of divisionsare to be made I doubt if it is practicableand it wil! be a case of equipping you rotarytable with dividing plates or obtaining adividing head of some form.

Some dividing applications are thoughequally, or more appropriate, for the rotarytable. Photo 16 shows a hexagon beingmade for a Iarge nut. The material wouldhave been too (arge to be held securely inth e th ree-jaw ch uck mou nted on thedividing head and so the rotary table withKeats angle plate was brought into use. Therotary table therefore coped with thesituation admirably and requiring only sixdivisions the table's dials were adequatefor setting each position.

Using a dividing head in its verticalmode and fitted with a facepiate for the task,Photo 17, would seem possible but it hassome severe limitations. Available heightin the machine and rigidity of the assembly,

especially the light nature of the faceplateare both Iikely problem areas. However, asmentioned earlier in the chapter, in thismode rotation of the cutter is endeavouringto unscrew the faceplate. It is not thereforea practical proposition and should not beattempted, even with a light cutl.

Mounting a workpiece onto the rotarytable, typically as in Photo 16, is not asSimple as first envisaged as it must beconcentric with the table. To do this markthe workpiece with a centre punch mark

,

Or centre drill, Then, place a centre in boththe rotary table and the machine spindieand align them as in Photo 1B using themachine's X and Y movements. Place theWorkpiece onto the table and tine it up usingthe machine's centre and clamp in position

,Photo 19. This should be accurate enoughfOr a!l but the most demanding situation

, in

this case final positioning can be set aidedby a dial test indicator and rotating therotary table .

Dealing with backlashDepending on the equipment being usedthere may be appreciable backlash in theassembly, but even with the more precisionitems it will not be totally absent. ln a11cases, it is advisable to take up backlashmanually by attempting to rotate theworkpiece in the same direction at eachdivision prior to Iocking the spindle readyfor machining. In some cases a length ofstring wrapped around the chuck,workpiece, etc. and weighted will performthe task automaticaily for you.

C hapter 4

The M athem atics

Before one gets down to producing theworkpiece it will be necessary to establishthe set-up required. The process is morecomplex than many will envisage, butfortunately the mathematics itself isrelatively simple.

The two central values when carryingout the required calculations are the worm/worm wheel ratio and the number of holeson the dividing plate ring being used. In the

case of a rotary table not fitted with adividing plate then the number ofcalibrations on the hand wheel dial will bethe important factor.

For commercial dividing heads 40 :1seems to be by far the most common, butin the case of rotary tables there is moreva r i at i o n , 4 O , 6 O a n d 9 O : 1 a I I be i n gfrequently available.

Dividing plates by nature of theirconstruction have more variation withsmaller plates having around 6 rings ofholes and larger ones 16 rings, maybemore in some cases. The smaller platesmay have a maximum number of holes of50 whilst the Iarger plates may have up to1OO holes. A smaller head is likely to besupplied with three plates making 18 ringsin all, a larger head will probably have 2plates with 16 holes making 32 rings in total.

Another factor is that dividing headsfrom different sources may be provided withplates having differing numbers of hofes ineach ring, additional plates also beingavailable to fill some of the gaps. This aII

1. Shop made dividing head having theability lo be used with differing worm/worm wheel ratios.

< - . . , - ' ' * * % #

adds up to considecable variation in whatis available and increases the number ofpermutations, making it impractical topublish in this book tables covering everypossibility.

Because of this and not having accessto tables covering a wide range ofsituations, I firstly decided not include anytables at all. However, l felt this wasunfodunate and have as a result developeda computer program to provide me with anycombination possible. From this I havechosen to provide tables for plates havingrings with 15, 16, 17, 18, 19, 20, 21 , 23,27, 29, 31 , 33, 37, 39, 41, 43, 47 and 49holes. These appear to be very comrnincombinations. Values have been workedout using these and three worm/wormwheel ratios 40:1,. 60:1 and 90:1. Havingprovided these iists they will be of particuîarbenefit to those who make their owndividing heads. The lists can be found inChapter 11.

l f p u rch a s i n g a n ew co m m e rc i a 1dividing head it will of course be suppliedwith tables for the dividing plates included,but will not cover any additional plates youmake or purchase Iater to fill in some ofthe missing divisions. A secondhand headmay also be missing its manual. lt is worthrepeating here that only the much moreexpensive universal dividing head will beable to provide aII divisions, at Ieast up to380. A semi universal head will Iikely beprovided with dividing plates that will giveaIl numbers up to 50 with progressivelyfewer the higher the number, typically 29between 51 and 1O0 but only 12 between3O0 and 380.

Some divisions consideredTo make the initial explanations as simple

as possible l have chosen to base theseon a combination of 60:1 forthe worm/wormwheel ratio and 60 holes in the dividingplate ring being used.

Consider creating a dial having 125divisions for use with an eight threads perinch (TPI) Ieadscrew requiring an anglebetween divisions of 2.88 degrees (360/125= 2.88), With the dividing head having a60:1 worm and worm wheel ratio and fittedwith a 60 hole dividing plate the rotationwill be 0.1 degree per hole movement. Ifwe consider 29 holes giving 2.9 degreesper division a small error of plus 0.02degrees will result. As the error will beaccumulative a final division of only 0. 4degrees would result, obviously far toogreat. Had the error been very muchsmaller then just possibly it may have beenpossible to Iive with it.

Taking now the requirement for a 127t00th gear, as used in an imperial to metricconversion on the changewheels for animperial Iathe. ln this case the requiredangle between each division is 2.8346456.Using 28 holes on the division plate wouldbe the nearest but as a gear is beingproduced any error at a11 will beunacceptable.

Other divisions will though be muchsimpler. One hundred divisions, as requiredon a dial for a 10 TPI Ieadscrew, wouldrequire 3.6 degrees per division, easilybeing accommodated by 36 holes on thesixty hole division plate.

How m any holes?The above examples serve to show that itis necessary to choose a dividing plate thatwill enable a requirement to be achievedexactly.

Let us fudher consider the 60:1 ratio

worm with a 60 hole plate. To rotate the R, H and D but what if attempting to workoutput of the dividing head one full out the number of holes (H) required onrevolution the worm will need to rotate 60 the dividing plate for a given division (D).times. As the plate has 60 holes this will In this case there are two unknowns (Theresult in the setting device passing 60 x 60 whole number, W and the number of holes,holes, that is 3600. Any whole number that H) making the process to appear less thandivides exactly into this is an achievable straight forward. However, the value for Wdivision. Taking an easy example, say 40 can be any number providing it is whole.divisions, this will require the setting device Consider the requirement for 57to pass 3600/40 holes per division, that is divisions in which the formula will read.80 holes, being one full turn plus 20 holes. 60 x H

W h i l st 36 0 O i s a re l a t i ve 1 y I a rg e W =number. the number of possible divisions 57is quite small and are aI( what one might The values for R and D, 60 and 57 incall simple numbers. These are 2, 3, 4, 5, this eyample, should be simplified to their6, 8, 1O, 12, 15, 18, 2O, 24, 3O, 36, 40, 45, smallest values, that is by dividing both by50, 6O, 72, 80, 9O, 100, 120, 150, 180, 200, 3, giving.240, 300, 360, 450, 600, 720, 800, 1200, 20 x H1800 and 3600. W =

t h e h e a d ra t i o 1 9K n o w i n g d i v i d i n gtogether with the number of holes on thedividing plate it will be easy to determine ifthe division required is achievable.However, you are Iikely to have a set ofdividing plates (or gears) that could resultin a lot of calculations, although simple, untila suitable dividing plate is found, or maybenot found.

On some occasions, your requirementmay not be covered by the publishedchads, or you may not have aII the platesquoted but have others. In this case youwill have to resort to calculation. Theessential requirement is that the dividinghead ratio (R) times the number of holeson the plate (H) divided by the number ofdivisions required (0) must be a whotenumber (W ), that is

R x HW =

From this it can be seen that W wi/l bewhole providing H is 19 or any multiple ofthis, 19, 38, 57, 76, etc.

Having established the dividing plateto be used it will be necessary to calculatethe number of holes traversed for onedivision. Assuming a plate having 38 holesis chosen, the number of holes for acomplete revolution of the workpiece willbe,

60 x 38 = 2280The number of holes traversed per

division will therefore be.2280

= 4057

Forty being achieved by one completeturn (38 holes) plus 2 holes.

w hilst 60 is a common ratio, 40 and90 are also common, (40 very common for

D commercial dividing heads).This is a simple calculation if one has Use for a dividing head in the home

. . . < . $+1.... . 5I. k..Id i1 f u .. .

workshop is Iikely to be Iimited and becauseof this purchasing an expensive commercialitem may be difficult to justify. Because ofthis the workshop owner may choose tomake one. Others may go down this routefinding the manufacture of a dividing headan interesting project in itsetf. One aspectof dividing heads made in the homeworkshop is that they may not have therestrictions inherent in those madecommercially.

The dividing head seen in Photo 1 isnot Iimited to a single worm/worm wheelratio as the design can cope with differingdiameter gears. Ratios of 30:1 , 35:1, etc.are therefore obtainable. Tlle simpler head,

essentially an indexer, shown in Photo 2can have additional gears added as inPhoto 3. This opens up possibilities thatare not available with a commercial unit.

T h e a d d i t i o n a I g ea rs i n P h oto 3amount to a reduction in angular movementbetween the dividing device (a gear in thiscase) and the dividing head spindle in thesame Way as a worm and worm Wheel.However, the ratio with a worm and wormwheel will always be a simple one 40: 1 ,60:1 , etc. W ith two spur gears though theresult may be complex. Typically, gears of60 and 20 teeth will have a ratio of 3:1 butgears of 45 and 25 teeth will have a ratio9:5. W hether this is usable will depend onthe number of positions on the dividingdevice.

The following should give an indicationas to what is possible. One important pointto make is not to work out the values indecimal terms as this can so easily shroudthe meaning of the answer, do stick tofractional form .

W hen calculating the results for adividing head, typically as seen in Photo

2. Simple single gear dividing head, alsomade in the workshop.3, the formula given on page 34, will stillapply. However, if a ratio of 9:5 is beingused this will go into the formuia as 9/5 andwould read.

9 x HW =

5 x DConsidering a requirement for 63

divisions it will read

W =5 x 63

Simplifying this by dividing 9 and 63by 9 gives

1x HW =

5 x 7Five times seven being 35, W will

therefore be whole if H = 35 or 70, bothstandard change wheel sizes. lncidentally,63 is a value not achievable with my 40 :1commercial semi-universal dividing head or

my 90: 1 rotary table. 63 is frequentlysuggested as a good change wheel to usein place of 127 tcrtb wbeel, being smaller,when cutting metric threads on an imperialIathe.

Som e More Exam plesExample 1Consider a set up with a 30 t00th dividinggear and a 60/20 t00th gear chain, that is3:1 . The formula is therefore number ofholes passed for 1 rotation of the dividinghead output is 30 x (60/20) = 90 holes. Thiswill enable the 30 t00th wheel to givedivisions of 2, 3, 5, 6, 9, 10, 15, 18, 3O, 45and 9O. Nine, 18, 45 and 90 being additionalto those which would be possible with the30 t00th gear direct.Example 2Consider a set up with a 50 t00th dividing

or rotary table.Example 3For this example I am suggesting a set upwith a 40 t00th dividing gear and a 50/30$00th gear chain, ratio 5:3, number of holespassed for one complete turn of the dividinghead output is therefore 40 x(5/3) = 66-2/3holes, (note we work in fractions). With ananswer of 66-2/3 holes the set-up wouldappear to be worthless, as no number willdivide into this. lf however in this case theoutput is allowed to rotate a further two turnsthen this results in 2O0 holes passed.

This will give a range of divisions butmost obtainable by easier gearcombinations. However, 200 will be usefulif calibrating a dial in half thou's for a tenTPl leadscrew.

With the workpiece (dividing headoutput) rotating three times it will be foundthat the divisions made on the second andthird rotation fall as required between thosemade on the first rotation. 1 was inclined toprove this mathematically but feel that thismay be overcomplicating the explanations.It will though work wherever a fraction of adivision occurs with a single output rotation.

3. Two additional gears fitted to the headseen J'r? Photo 2 giving a greater range ofpossible divisions.gear and a 75/30 t00th gear chain that is15:6

The number of holes passed for onecomplete turn of the dividing head outputis therefore 50x(75/30) = 125 holes. Thepoint to note here is that even though theratio is 15:6 it still results in a whole numberfor the number of holes. Available divisionsare only 5, 25 and 125, but 125 is usefulfor calibrating a dial for an 8 TPI (threadsper inch) leadscrew. Again this is notavailable with my commercial dividing head

v , A

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Example 4As a more extreme example, a combinationof a 40 t00th dividing gear and a pair ofgears comprising 45 and 35 giving a 9:7ratio and 51-3/7 holes. Seven completeturns will therefore give 51-3/7 x 7 whichequals 360 holes passed. It can thereforebe used when calibrating a rotary table indegrees.

These examples, which show only aminute fraction of those possible, do, lhope, give an indication of the range ofpossibilities with this set up, and as a resultenables you to go down this avenueknowing that it ls possible.

Forthe sake Gf simptlclty l have ignoredthe effect of using a forked detent and forconsistency with other explanations, havereferred to holes when using gears as thedividing device; the slot between twoadjacent teeth will of course be used. I havea I s o u s e d f o r m y e x p I a n a t i o n s ,changewheels having increments of 5between sizes, 25, 30, 35, etc, I do realisethat a few Iathes will use other increments,typically by fours. W hiIst the results will bedi#erent the methods wilt still apply.

plate errors. The extent will no doubt comeas a surprise to the uninitiated.

Consider a division plate with 18 holestheoretically spaced at 20 degrees (360/18 = 20), but having an error of 1 degreeon the 12th hole, that is spaced at 19 and21 degrees between its adjacent holes. Ifnow attempting 9 divisions (4O degreespacing) and using a dividing head with a6O: 1 ratio, the arm on the dividing head willhave to pass 120 holes per division, that is60 x 18 / 9. This is 6 complete rotationsplus 12 holes ((6 x 18) + 12 = 120) for thefirst division.

l n this example, input rotation willtherefor be, (6 x 360) + (11 x 20) + (1 x 19)degrees, that is 2399 degrees for the firstdivision, and for the next division, (6 x 360)+ (11 x 20) + (1 x 21 ) degrees, that is 2401d e g re e s . A s t h e w o r m /w o r m w h e e Iarrangement reduces the rotation by afactor of 60 the angles at the workpiece willbe 39.984 degrees (2399/60) and 40.016degrees (2401/60). From this it can be seenthat the second division will be accuratelyplaced as it compensates for the error inthe first, (39.984 + 40.016 = 8O) but the +/-1 degree error between the two on thedivision plate has been reduced to 0.016degree, 1/60th that on the dividing plate.The value of 1/60th is no coincidence butwill always be by the same factor as worm/worm wheel ratio.

A feature of this is that even platesmade in the home workshop by relativelyinaccurate methods will still produce resultsaccurate enough for aII but the mostdemanding requirements. Even here youcan use the dividing head to make a secondplate and use this for producing the finalproduct. By this means you will benefit fromimproved accuracy twice over.

37

Further detailsChapter 7 includes a design for a simple,three gear dividing head and fudher detailsregarding the mathematics of using such adevice. A Iist of divisions possible is alsoincluded in Chapter 11 based on a set ofchange wheels of 20 to 75 by five's.

Division plate errors m inim isedW hiIst not a calculation that the reader

will be called to carry out, the followingillustrates how a worm and worm wheelconfiguration (or two spur gears in a gearchain) reduces the effect of any division

jj I v.1 l . I

. II ' .!1 I?

'

( Ii I!1 (p - 1) x 360 ,:5 . -y: -' ;

1111; ,i r v = R sin --------------- x2 p k)'' I//J *

N4 .1j calculating these values, even when there 7 ..- .1 .1

I 1. . are many more holes, will not be thatI i' J ' arduous if yOu have a calculator having 3 . i/1 l . z

zw

yzI'I * je alcu latl n 1 trigonometrical functions. unlike printed .!I. O-or l na tables that normally list values up to 9o 75I'j j)j ' degrees a calculator will deal easily with 1) ? ..

'II I i the angles above 90deg., giving the value ..--''-'

I . yjI and whether it is positive or negative. I1 I i . ou ld suggest th e refore that a basic 1'5i j . w

4 (flpf scientific calculator should be a standard --.I11 item in the home workshop. Even better. oqIGIN g. II. This will be to setthe dividers to the radius, would be to obtain a programmable k = gJ'j/r ). Holes on a Pitch Circle scribe a circle and then with the scriber still calculator, in this casejust enterthe formula Y' = 0 --ï4 - k5I L' r Diameter (PCD) at the same setting step round the scribed once, then enter sequentially the variables FIVE CICCLES 0$ A FITCH CIFSLE DIAkETE8'j ;

(lytgjj Ar rgyyyg rr yjrcjj cjycgg yjAagrgy,' k The mathematical method. circle. Many applications will though be (P only in this example) to arrive at eachI' /1// r The need to place holes on a PCD can much more difficult than that and another required value. SK1f

.I! laod will be needed. A disadvantage of the method in sK.1.' h ! occur for many different reasons but most met' 11 .

. 11 number of One such method is to work out the isthat it involves b0th positive and negative negative value creating a minus minusj, often only involving a sma. IJj2 ; holes, typically 3 or 4 when drilling a back position of each hole in terms of its X and Y co-ordinates making it somewhat difficult situation, mathematically this equates to a.1

In modelling co-ordinates and uses the milling machine to equate the values to those to be read off plus situation. In simple terms 5 - (-3) = 5 +I j plate to take a chuck.I!I ials to position each hole. The the leadscrew dials. This can easily be 3 = 8.engineering 5 or 6 holes to fix the cylinder leadscrew d

i ; be advantage of this method is that it achieves overcome by changing the reference point Some may say that holes below theI 11 1. coveron a stationary steam engine may .

f f ( The obvious first choice for positioning a high degree of accuracy, aiso any number from the centre of the circle to a point equal upper line should be negative if norma!l II' I jI I head or of divisions is achievable, except of course to the extreme upper and Ieft positions as geometric conventions are applied

. This' I the holes will be either a dividingI I ' I rotary table, However, some workshops will for a practical maximum. Before this can in SK.2 making aII co-ordinates positive. may be correct but my comments relate to1) I J I : Iff f fl not be equipped with either of these and be undedaken the positions of the boles The required co-ordinates are easily arrived increasing values being read on the. I I :1. )1 even if they are they may not adequately need to be calculated. SK.1 shows a very at for X by adding the radius of the PCD to Ieadscrew dials. Adrill placed over the zero11

: I I supporttheworkpiece, eitherdueto its size, simple example requiring to position 5 holes each value the formula for this reads: Iinewill move towardsthe Iower holes when'IJflj /1 weight or sbape. Also, even if a semi on a given diametec (P - 1) x 360 PCD the hand wheel is rotated clockwise and1.1. I'' universal dividing head is available many X = R Cos + + - the reading on the dial increases. However,Iill. ' bers over 5o will not be achievable. The Form ulae N 2 some milling machines do not conform toI 11 num.'IIiIk situations will therefore arise where an The formula for the X co-ordinates is ForY howeverthe value arrived at must be this standard and the datum pointwill havesli '

.?: hod uas to be found. (P - 1) x 360 taken from the radius of the PCD, the to be other than in the top Ieft as in SK2. It11111 alternative metI

probablythe mostlikely requirementwhere X = R Cos formula therefore reads: will not though alter the calculated values,I I I1. I a Iarger number of holes are required will N PCD (P - 1) x 360 only iaow they are applied.' be to make a division plate, required, but where R equals the radius (that is PCD/ Y = - R Sin -; '. not presently available in the workshop, 2) P equals the hole number, e.g. 1, 2, 3, 4 2 N Hole generationI

D take note that the value for R Sin ((P-1) A variation is often used in the homeOne of the commonest alternatives will or 5 and N equals the number of holes, 5 obe when the requirement is for six holes. in this case. Similarly for the Y co-ordinates x 36O/N) for some hole positions will be a workshop to enable large holes to be cut in

38 39I

I 1II I

' tQ.- - . - - . .

' . a ..:..â1k. '

be drilled. However, do make the numberdivisible by 4 as this will make the holesidentically positioned in each 90deg,segment and as a result reduces theamount of calculation required appreciably,

Having decided on the number of holeswork out the angle (A) between eachadjacent hole, that is 360/N where N is thenumber of holes. Chose an outer diameter(D) just sufficient for final finishing. The drilldiameter (d) can now be calculated usingthe formuia in SK3. If the drill works out toosmalj, or too Iarge, then reduce or increase

!

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N

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)AN

AhGLE 8ETAEEN THE FOLESNUkBEF 0F HOLESOUTEq CIAMETEF

dFC ()

EIqILL DIAMETEFFCC ON AFIICH FICLES A9E7'0 8E ZiILLED

a workpiece by drilling touching holes on apitch circle as illustrated in SK3. WhiIst thiscan be done using relatively inaccuratemethods it almost certainly will result in theneed for more manual activity - filing,sawing, etc.

I n t h i s ca s e t h e P C D i s n ot ofimportance, what is, is the diameter on theouter edge of the drilled holes. The closert h i s i s to t h e u I t i m ate h o I e s i ze w i I Iconsiderably minimise the finishing worknecessary. W hat is required is, that withthe chosen hole size and on the calculatedPCD, that the outer edge is close to thehole size being made. This may seemrelatively straightforward but the drill sizeand PCD have to be chosen more carefullyand involves some calculation. Havingstaded on the project I had anticipated thatthis may prove quite complex but in fact itis not that difficult, AII that is necessary isto roughly estimate the number of holes to

40

:5 60A = - - - -

N

SK3

1. Using X and Y ' t. , );. y

co-ordlnates tomark out position 'f holes to remove 'Othe centre Of a f :, '. ')

.

rotary table body. 'This to take the . ,table 's bearing. 't 7?1

q) -

(5 y . .: ' ''?! lrîlt ''t/''' . ,it-.'). ... h;;'î.c 77. . q nyj . 2 ,.,; , q t 't..y rj y;.@#k,,. . . ;y; IL jj

g y. j y. y. k ! . .' .. @t ?-.. ; .ï.ax$. j.yyyyty.(,l?- . ) t ' . j .. , , ). . .

the number of holes estimated andrecalculate. The PCD on which the holesare to be drilled will be equal to D - d. Theco-ordinates can now be calculated as inthe first example and then drilled,

I used this process when needing toproduce a Iarge hole in a casting. Photo 1shows the hole positions being initiallymarked out. After drilling it was verygratifying when the centre just droppedaway as the Iast hole was drilled, Photo 2.This made the care taken well worth theeffort involved.

W hen adopting the above approach itis likely that in many cases the anglebetween each hole will be a complex value,it will though be of no consequence if theprocedure is adopted fully. However, if thenumber of holes is chosen to arrive at awhole number for the angle, (say for 36holes, 360/36 = 10 degrees), then a rotarytable could be used if available as theIimited calibrations on a basic rotary table

will easily cope with sucb angles. ln thiscase a1I that will be needed is to calculatethe hole diameter and the PCD.

Using a com puterHaving suggested using a programmablecalculator, even better would be to use acomputer spreadsheet program. This wilinot only produce the complete Iist of valueson screen but will also enable a printout tobe made for use in the workshop. If youare an accomplished user of spreadsheetsyou will not need me to inform you of theadvantages of using these for repetitivecalculations. If though you have a computerthat you ably use for other applications mayI encourage you to get to grips withspreadsheet applications.

A spreadsheet is basically a formdivided into columns and rows and at eachpoint where they cross a block is created,called a cell, Columns being referenced A,B, C, D, etc,, and Rows numbered 1 , 2, 3,

x r ' j jI v, ' I j1 ;.

.

I Il -I

j jj 'j'l 2. The centre fell Initially cells A2 and 82 will be Ieft blank probably be 8 characters wide, 5 for wholei. I away as the final wjth cell 02 having the formula for the pounds, 1 for the decimal point and 2 for

@'f '' fl hole was drilled, a volume of a cylinder added. However, the the pence. The column to carry the itemfI I - .I ' very satisfactory formula Will not appear in cell C2 so the description will be set up for text and haveI - 1 , .I I 1 conclusion! sheet will initially appear as above. The a much larger width, say 30 characters.

'ilj j' ' formula will then appear elsewhere on the l should explain that in addition tofIf . t11 I I creen, normally on the Iower line, but only providing cells for inputting values andl / Spr ' ' j when the Screen CUrSO: iS glaced in that others Containing formula, heading cells areI 1 I -.1.1 , cell. The formula, Volume = T:xR2xL will also included at the spreadsheet design

7 p stage. The oiameter, Length and volumej f .,r..k ..:. - though be set up in terms of cell references' ' d Will therefore be lx(A2/2)2xB2. Most, if headings in the above are an example,: an''' J ' r'ot all, Computer programs use * as the ' have above presented the formula in/2 /

ingle line format, rather than the easier to.#' ' multiplication sign so the formula will read Sj , understand multi line format used earlierjj , a.(sry,;,.:z. sjnjs js a very simple in tje chapter

, as this is the way formulae, . ,,j , jjoatjon uut one that would be very well iII have to be entered into theil F ' ' app -'17.7 ' 4 etc

.

Typically therefore a cell in column it maybe a single calculation from a very Worth setting up if you are a new comer to W dsjaeet.p

, sprea

'@' c and row s will be referenced c5. Iarge numberof entered items, typicallythe Spfeadsheets. You will soon find theI .j j ayvaotages of being able to enter new M ultiple calculations; Each cell is established for a single total money spent on items purchased overj vajues for diameter and or length and for

vjae spreadsheet really proves its worthIlji p purpose being chosen from four available a period of time. On the other hand it may

ke a multitude of calculations from a tbO Volume to appear immediately, wjnere multiple calculations are involvedjlf j uses. ma jjwe now enter a diameter of 10 and a and where there are many more columns1 . To carry text entered at the spreadsheet small number of entered values. In thisj ; joyjgtjj oy g tjjo soraas wkjj reatj

(y rows, sjje rjeetj to cajctjjate x and Y$ l design stage and used for such purposes chapter, calculating all the X and Y co- an1Ilg as a heading for the sheet as a whole or Ordinates from just two entered values, the ' '>. , B c n co-ordinates at numerous angles is a good'fIII ' headings for individual columns. number of holes and the diameter on which 21 lyj)yvq Yeso l ******1 VWUYE example. However, unless you are exped2 157, $.Ii1 I 2. To carrv text entered when the these are olaced. a:th. '' in setting outtheformula itwill be necessarv'.1 1. ' It is s 'uch a case as this that makes the to proceed systematically. Let us take th-ejI.I:.I. soreadsheet is used. In a financial11/'J1.'tt a'oojication this could be the descriotion of use of soreadsheets so useful in the home -n lf t,he itrogram ,cursor is placed on C2, slightly more complex examnle of workina'fI'I'' .1 ' ' ' ksh 'op. The speed at which this takes 'ROR O'SeWrlere on tne screen the formula out the touching holes o'n a PCD aWs.111 I an item purchase. wor' ' 1. a To receive numerical data as the sheet place can be a surprise to a new user of a fOr that cell, 'n * (A2/2)2 * B2 will be illustrated in SK3

.l I . 'jl j I . displayed, whilststill displaying 157.1 in the First the hole diameter must bei . I . is being used. Again in a financial personal computer, add new values forthe ,

'?')' 1) application tlnis could be tlae value of an number of laoles and the PCD and the list. calculated based on the outer radius andjggpfj; zjje program will calculate, in the the number of holes chosen, ln addition toI . i item purchased

. required values will appearalmost instantly.'' i 4 To display numerical values calculated background, the answers to very many headings

, etc, set up at the design stage,I I I .il '!I by the spreadsheet using the values Give it a try decimal places but you can format each four cells must be provided as follows::.j: j cojumn to display values with the number 1 For the number of holes chosen.f. ? entered as in 3 and using formulae entered The following is an example of a simple .I,j of decimal places as appropriate to the 2 For the outer diameter

....111 . by the sheet designer at the spreadsheet spreadsheet set up to calculate the volume .E' I design stage.

of a cylinder where the user adds both its Zp/lication. All columns can be individually 3. The cell in which the program displaysI I'. There can be many entry cells and diameter and length. configured in terms of width, number of the calculated value forthe angle between

1 'I' formulae giving many output values. lt is , . o - decimal places, etc. In a financial sheetthe adjacent holes.' ' these calculated values that make the , Dl- e'reR ue- nf Y'voo-ze - Column forthe value of the item purchased 4. The cell in which the program displays

dsheet so useful. ln a financial sheet 2a Will be set up for numerical data and the calculated value for the hole diameter

.sprea

/42 43

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= in (cz/zland f in the case of the word ''holes'' ''number COS((P-1) X 360/N). To make the formulaecetl's A2 and 82 should be set up for Changetheformulato read s jI il laough R, p and N will have to be'! ' 1. ical entry and c2 and o2 having the check this against some trig tables or your f holes'' was preferred then the heading Work t

. numer o! Ii' scientific calculator. The brackets ( ) are ould span rows 1 and 2 with the value Substituted with the cell references for theI I formulae for calculating the angle between c' I essential elsethe programwill giveyou half being allocated to row 3. The columns do CelIS containing the values.

ffj j I the value of sine C2 that is quite different ot have to be wide enough to display the: A B c D 011 I from the sine value of half of C2 being what formulae, these are displayed separately Dklplicate and PasteI!i' I 1 HOLES OD ANGLE DRILL Slz.E

jl 'I2 , ,'j 2 is required. The brackets say do C2/2 prior nd one at a time as the cell is selected. If you set up your spreadsheet for up to! I 3 a

I i .. to choosing the sine value. 'rhe two screen prints help to illustrate this, 1O0 holes, or more, you may feel that typingI .III I I Again enter edit and change the ore Iater

. in the formula 1OO times and similarly fori holes and the drill size. As already stated mI)gf/ the formulae dp not appear in the cells but Ormtlla to read = 1/(sin(C2/2)) and check lf carrying out the above was to be a the other three columns, is a task beyondI II I k eisewhere on the screen. l should add at tbat the Vaiue 1 divided by sin(C2/2) is the one-ofcalculation then you would be better what is acceptable. Fortunately, the' j

'

I I r: tjais stage that as with aII computer COSUIt, take note of the extra brackets. with a piece of paper and your calculator. If facisities ''duplicate'' and d'paste'' Iimit thel, there will be subtle differences Continue going through the following though you were expecting to make the work involved considerably. Having typedIII kk programsI ,, px... .la.. pxcaoio rxriraoïralo. i'aair-ntoa in tlaiq sequencechecking thevalue ateach stage, calculation frequently then save the sheet the formula in for a single Iine and checked

IIIj J' )J k'p-'at t,''= <'v.=->' L .,''' ''' ,:-'F?.u'-- '--'----- '- -- - next = (1/(sin(c2/2)))+1 and finally, = B2/ to a file and call it up next time you need it, that it worked it could then be duplicatedI '. C'Iapter snou.w opp,y. j/(sin(c2y2)))+j )

, vjais may seem a slow a1I that will be needed would be to entef into the remaining 99 cells. However, afterEf ,' ' Building up a formula for adding to a ((!, I k, rocess but as the value appears newvaluesfornumberof holesand/orouter having duplicated say 4 individually the! cell can be somewhat complex as the P!.i formula has to be entered as a single Iine immediately the formula has been edited, diameter. ln any case, as mentioned above, block of 5 could be duplicated and pasted! .

)l ' d the correct usage of brackets observed it is no more that a couple of minutes. even for a single application you may have in five at a time reducing the worki.I: , an;I' ' to ensure that parts of the formula are Entering the formula at one go and Ieaving to carry out the calculation a number of significantly.p '$ out a crucial bracketcould take much Ionger times to arrive at a suitable hole size

. Thisthough is notthefuil story aswhilst, calcusated in the correct order. By far theI I . to solve, of course if you are experienced As already mentioned, the real benefit the values for R (radius) and N (number ofiI' ' best way is to build the formula in stages

I 11 i' d observe thatthe correctvalue is arrived FOu then enter it a one go. of using a spreadsheet becomes apparent holes) are constant, and will be picked from. r anI , t each stage. One fudher point regarding the above, where multiple calculations are required the cells at the top of the sheet (R is in C11I aIII , starting firstwith the easy one c2. The FoUC Spreadsheet may use radians rather with the need for multiple X and Y co- and N is in A6 in the screen print 2), the7r2Ij,'r. formula for angle A is given in sK3 and than degrees so the above formula will ordinates being an excellent example. value for the hole position ''P'' (A16, A17,1.11..1 d adjusting to suit. For the reader who yive columns will be needed as follows: etc

.) progresses by one on each row. AII isI I ' hen placed in cell c2 would read = 36o/N neeI I WIII is not familiar with radians, 360 degrees column A. Hole Number. not Iost as when the formuia is pasted forI ' I where N being the num ber of holes.

1. : I Is 2 x 'n radians, In this case sin(C2/2) Column B. X co-ordinate relative to the the first time, the program will seek out each1111 j However, the value for N will have been equa11 1 ould read circle centre. variable and ask if it is absolute (the sameI '' : entered in cell A2 therefore the formula in W

I / Ji . . c2/a6o)/2) column c. Y co-ordinate relative to the value each time) or Relative (changes eachfI;(I c2 should read = 360/A2. Note that / is sin((2 J:.1 .1!1 I d for divide and * for multiply in cells A2 and B2 have been set up for Circle centre. time relative to another cell). Havingi I u s e' il i spreadsheet programs. numerical entry and could be 3 characters Colum n D. X co-ordinate relative to indicated that R and N are absolute and P' I ! I

' ' 1 The formula in D2 is though much more for A2 (up to 999 holes) and 7 characters extreme co-ordinates. relative it will not ask when the formula is'

I I ,, c lum n E v co-ordinate relative to pasted in furlher cells so the task is still an! i I complex being that given for ''d in sK3. for 82 (up to 999.999 for the outside O .p . Build this up in stages starting at tbe diameter). However, width of columns will extreme co-ordinates. easy and quick one and can be done infi 'rhe formulae for these will be those blocks rather than one Iine at a time. Do' j innermost expression, that is A/2. Now often depend on the heading required at' I remembering thatAtthe angle) is the value the top. For example column A may have included in the paragraph headed ''The though set up only a few Iines and test yourI

in cell c2, therefore entertheformula = c2/ to be 7 characters wide, that is five for the Formula'' on page 38. Theywill need to be program thoroughly before pasting in the2 and observe tlaat the result is half the word ''holes'' and a space either side to Written on a single Iine with aII the brackets full number of Iines.angle io c2. separate it from its adjacent heading. in the required places, typically for the X This still has the column ''A'' which

Enter the edit mode for the cell and Headings can take up more than one row. Co-ordinate relative to the circle centre = R contains the hole position number. 1f, for

44 45I

I

- L -Q- x

. . '... 1.:

r

A B C D1 CALCULATES CO-ORDINATES OF HOLES ON A PCD

3 USE: ENTERED ITEMS4 NUMBER OF Radius at5 HOLES hole centre6 5 40.000

8 CALCULATED VALUES9 Angle1G Between holes11 72.000

13 RELATIVE T0 RELATIVE T014 CIRCLE CENTRE EXTREQE CO-ORDINATES15 HOLE NU#BER Ce-ordlnate X C/-ardlnate Y X Y16 1 40.000 0 80.000 40.00017 2 12.361 38.042 52.361 1.95818 3 -32.361 23.511 7.639 16.48919 4 -32.361 -23.511 7.629 63.51120 5 12.361 -38.042 52.361 78.04221 0 0 0 0 0

B16/F@rmu1a: IF(A16jC6*C0S((A16-1)*(((2*PI)/360)*C11))jO)

CREEN PRINT 1

example, you are working to a maximumnumber of holes of 1OO in which case youcould just type in, when designing thespreadsheet, the numbers 1 to 1OO downcolumn A. Thîs would work quite well butwhen requesting co-ordinates for say 10h o I e s o n a P C D i t w o u I d co n t i n u ecalculating through the 100 Iines as thoughyou were going round the circle 10 times.When on the screen the lines beyond 11up could be ignored but if as is Iikely aprintout is to be taken, extra sheets wouldbe printed out. If therefore the sheet couldbe made to stop at hole 10 an aII roundtidier situation would result.

Rather than just typing 1 and upwardsit could be arranged for the formula to dothis. Taking screen print 2 as an examplecell A16 would just have the figure 1 typed

in. Cell A17 would though have the simpteformula = A16+1 . W hen pasting in furthercells and requesting these to be relativewe would get, = A17+1 , = A18+1 , etc.

Having now arrived at the hole numberby this means it will open up the possibilityof extending the formula so as to halt theprogression at the number holes required.However, to do this will involve includingsome logic expressions in the formula andthis will increase the complexity quiteconsiderably and if new to spreadsheets itis best Ieft at this stage. W ith this done theprogram will calculate the values for thenumber of holes required but then continueas if going round a second time and more.

To achieve a tidy result it would thenbe a good idea to copy the file to anotherand in this block delete aII the records

CALCULATES CO-ORBINATES OF HOLES IN AN ENCLOSEING OUTSIDE BIARETER

USER ENTERED ITEYSNeMBER OF QUTERHOLES RADIUS

5 0.650

PROGRAR CALCULATED ITEMSHole diameter Radius at Angle

0 hole Centre Between Holes1 0.481 0.409 72.000

3 RELATIVE T0 RELATIVE T04 CIRCLE CENTRE EXTRERE CO-ORDINATESs BOLE NUQBER Co-ordinate X Co-ordinate Y X Y6 1 0 .409 0 0 .819 0 .40917 2 0 . 127 0 . 389 0 . 536 0 .02018 3 -0 .331 0 .241 0 .078 0 - 16919 4 -0 .331 -0 . 241 0 .078 0 .6500 5 0 . 127 - 0 . 389 0 .536 0 . 7991 0 0 0 0 0

l6/Fermula : IF (A16 ,C1 1*C0S( (A16- 1 ) * ( ( (2*PI ) /360) *D1 1 ) ) j 0)

CREEN PRINT 2

above the values required. This could then following should give an insight into thebe printed out for use in the workshop. The subject.sheet would still contain the formulae up to Consider colu mn A, carrying thethat value and could be used again with rumber of each hole, this could be set upthat number of holes for subsequent with some simple logic that halts theapplications. calculations once the hole number has

reached the number of holes required.

Logic Trying to express this verbally the IogicW ith this we are now arriving at a much would state, ''IF the value in the previousmore complex use of spreadsheets and cell equals the number of holes requiredone that most will never see a need to use. enter 'dO'' IF NOT enter a value one higherI would therefore suggest that unless you than in the previous cell.are conversant with Iogic expressions you W hiIst this would work for the first Iineleave your sheet at this stage. Eventually, after completing the number of holesWhen becoming fully conversant with Feguired it would not work for the next lineSpreadsheets this far, you could then take as the previous value would not equal thetime to Iook into the logic provisions of your number of holes required but would equalprogram, However, rather than Ieaving the nought. It would as a result add one to thisSubject without any further explanation the Starting the sequence again, because of

46 47

. ' >

. . . I kI,

this a multiple IF has therefore to be used.This would state ''IF the value in the abovecell equals ..0'' then enter '.0,' IF NOT IF1 1the value in the previous cell in the columnequals the number of holes required enter.'0'' IF NOT enter a value one higher than inthat ceII''.

To ensure that the X and Y values alsodisplay a value of zero the formula shouldinclude an IF clause as illustrated at thebottom of the screen prints if this were notdone the co-ordinates would be worked outon basis of zero in column ''A'' givingi r re I eva n t v a I u e s . F ro m t h e s e b r i efcomments on the use of logic it can be seenthat the com plexity has been raisedsignificantly. Please do not however 1et thisput you off attempting to use spreadsheetsin their simpler form.

Screen PrintsI will finish with a few brief comments onthe screen prints published. Screen 1 isfor calculating holes on a PCD whilstScreen 2 calculates values for holes in anenclosing circle.

The only major differences are that in2 t h e h o 1 e d i a m ete r ( B 1 1 ) h a s b ee ncalculated by the program as has the radiuson which the holes are to be placed (C11).

It is not visible on the print but thecursor was at cell B16 when the screen printwas taken and the formula for that cell isdisplayed at the bottom left of the screen.Moving the cursor to other cells wouldcause their formula to be shown. Note theIF command that basically states IF A16 iszero display zero in B16 IF NOT thencalculate as per formula.

One other important point worth

In their simplest form spreadsheets arenot that complex and yet still very usefuland time saving. They also avoid anypossibility of errors due to tapping incorrectvaiues into your calculator, easily donewhen many hundreds of calculations areto be carried out. So what are you waitingfor, go on, give spreadsheets a try.

repeating is that your spreadsheet may useradians to describe angles rather thandegrees. Therefore, as there are 2 Piradians in a circle then say f0r 70 degreesthe number of radians is 70*2pô/360. Thisshould be evident in the formula for B16.

The screen prints also illustrate anotherimportant feature of spreadsheet design.Considering screen print 2 it can be seenthat Iines 3 to 6 are used for date inputedby the user with the remainder displayingvalues calculated by the spreadsheet.These though can be divided into twocategories, iines 8 to 11 displaying valuescalculated the once only whilst Iines 13u pwa rd s re p e at b a s i ca I I y t h e s a m ecalculation but for each hole position.

Of greater significance is that when acolumn has been allocated a width anclformatted (number of decimal places, etc.)this will apply to aII items down the column.Typically, had ''Outer radius'' been placedin A6 and ''No. of Holes'' in C6, holenumbers would have to display as 1.000,2.000, 3.000, etc. and number of holes as5.000 - this can complicate the design ofsome sheets. Having made the point itmaybe that some more modern andadaptable spreadsheet programs do allowcharacteristics of a column to change downtheir Iength.

G hapter 6

S im ple S ho p-m ade D ivid ingDevices

The next four chapters deal with items thatcan be made in the home workshop. Thereasons forthis approach will be numerousbut are Iikely to be mainly.1 .The workshop owner gets muchsatisfaction in making workshop tools.2. Because of limited use cannot justify theexpense of a commercially made item .

3. ltem not available commercially.Some of the items in this chapter, along

with the Lining tool in Chapter 9 are

examples of items not availablecommercially. It is assumed that any readerembarking on projects involving dividing willhave arrived at a reasonabie understandingof basic workshop practices. Because ofthis, details of manufacturing techniqueswill be reserved Iargely to areas of greatercomplexity,

Lathe mandrel gear m ountingThe method of mounting a gear on the rear

1. The two partsthat make up theIathe mandrelgear mountingassembly.

48 49

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50

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end of the lathe spindle for dividingpurposes is shown in the publishedassembly and parts drawings. Nodimensions are giver as they will vary fromIathe to lathe.

Manufacturing this is straightforward,place the material in the chuck for the outerpart and with sufficient projecting tomachine the whole part at this stage. Useleft and right hand knife tools to machinethe two parallel podions without removingthe part from the chuck ensuring as a resultthat they are concentric. Set the angie ofthe top slide and make the internal taper,Ieaving the top slide at this angle for theQther pad. Next machine the parallel portionOf the inner pad making the thread also.

Turn the pad in the chuck holding on theportion just turned and machine the taperPhoto 1 shows the two pads on completion.

I am not including any details for thedesign of the detent mounting as themethod of mounting this wilt vary widely.Bowever

, using the changewheel quadrant

would seem a good starting point forconsideration. The plunger in the detentassembly should be made a close slidingfit in its housing so as to minimise backlashwhen in use. Despite this, backlash shouldalways be taken up manually and in thesame direction, even with a precisiondividing head. Again l have not includedany details for the detent assembly butthose in Chapter 8 (parts 41 and 42) shouldprove a basis for any design.

Slitting the outer component isillustrated in Photo 2 and as can be seen itis a simple operation for the dividing head.However, it serves to illustrate a feature ofthis form of head which has not beenmentioned so far. Just visible behind thechuck is a plate containing a ring of 24holes. This permits direct indexing of anydivision possible with a 24 hole plate, thatis 2, 3, 4, 6, 8 and 12. The head is stillrotated via the worm/worm wheel from themanual handle but is Iocked in place usinga peg in the top hole position. The peg is

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advanced using the small Iever partlyvisible top right of the dividing head.

Photo 3 shows a typical assembly, butdo not be confused, due to Iack of spacethe photograph has been taken via a mirror.

Bull wheel detentThis is another case where the design willdepend very much on the Iathe to which jtis being applied. However, once again thedetent assembly in Chapter 8 should provea basis. Photo 4 shows the method appliedto a Myford Series Seven lathe.

5. A chuck back plate being prepared fordrilling holes for dividing purposes on the

Iathe.

make it difhcult to avoid the back plate'sfixings.

Dividing platesHaving a semi-universal dividing head anda good range of dividing plates there willstill be many divisions that are not possible,even at Iower numbers. Typically a need of53 divisions can only be achieved using adividing plate having 53 divisions itself. Asthis is a number greater than is normallyavailabte on the smaller plate sizessupplied, another plate would have to bepurchased, lf also it is for a one offapplication such an expense may bedifficult to justify. Making ones own maytherefore be the way forward.

An interesting feature of using adividing plate via a worm/worm wheel withthe same number of holes on the plate (53in this example) as there are divisionsrequired, is that the number of holestraversed will always be equal to the wormratio. Assuming a ratio of 40:1 the numberof hole traversed for one turn at the outputwill be 40 x 53 and the number of holestraversed for one division will be 40 y 53/53 = 40. This would be achieved with oneturn plus 13 holes.

Having mentioned 53 as a division andStating that it can only be achieved with a53 hole plate, I should point out that this isbecause it is a prime number. Unless aUniversal dividing head is available, ratherthan a Semi universal head, prime numbersalways require a plate having the samenumber of holes, excepting for Iowernumbers where a multiple may be practical,typically for 19 divisions a 38 hole plate.

FoI more information regarding primenumbers see Chapter 1O.

3 Above. A typical detent mounting, it willof course t/aly depending on the Iathe towhich it is being fitted. Because of Iimitedspace this photograph has been takenvia a mirror.4. Below. Bull wheel dividing attachment.

Chuck back plate dividingW hiIst not applicable to today's workshopsto the same extent as in the past, dividingusing drilled holes around the chuck'sbackplate can still have its place. Drillingthe holes may though seem a daunting taskbut as the system is really only appropriatefor Iower numbers there is no reason whythis should be. Using the method of adivided paper strip, as described in Chapter3, will make the process an easy one.Photo 5 shows a chuck prepared for twelvedivisions. The back plate is to be centrepunched on the markings and then drilledwith tbe required holes, 3 mm diameter and3 mm deep would be about right. Care inp o s i t i o n i n g t h e m a rke d st ri p w i I 1 b enecessary to ensure that the holes do notconflict with the back plate's fixing as theymay be close to the edge.

Having also divisions of 5 and 10 maybe desirable in which case a ring of 60 holeswould appear to be required. This need notbe the case as two rings of holes, one of10 and one of 12 could be made. ln thiscase, positions 1 and 7, from the 12 holering, sharing the same places as holes 1and 6 from the 10 hole ring. It may though

52

Using X and Y co-ordinatesBy farthe most accurate method to producea division plate would be to work out the X& Y co-ordinates and use the millingmachine to position the holes. Forthe lowernumbers this would cedainly be the way toproceed but for higher numbers the methodcould be a little tedious and great carewould be needed in setting the table'sposition for each division. As a precaution,Iightly mark out the positions with a centredrill and inspect the result before removingthe plate from the table, Any obviously outof position hole can be set up again usingthe available co-ordinates, marking again,this time with a Iarger centre drill, Do alsomark the plates centre position whilst onthe table as concentricity of the mountingposition is impodant.

Using a Rotary tableUsing a rotary table would also be worthconsidering and where possible be asaccurate as using co-ordinates. The Iimiting

53

I . zlklla

factor would be if the angle betweendivisions could easily be established usingthe table's calibration. Typically, a need for45 divisions would require an angle of 360/45 per division, being 8 degrees, W ith a60: 1 ratio worm/worm wheel this wouldrequire, one turn (6 degrees) plus 2 wholedegrees using the table's calibrationmaking it a practical proposition.

If the need is for 46 divisions, at firstsight a relatively simple requirement, theangle between divisions would be 360/46,being 7.826087 degrees. This would beone turn plus 1 .826087 degrees on theta b I e ' s c a l i b rat i o n f o r e a ch d i v i s i o n ,obviousiy an impractical proposition. Usingtbe rotary table bas therefore limited usefor making dividing plates.

However, as a last resort, a Iist of

54

6. A 125 dividing plate made using anactual size CAD print.

values from the star't could be produced7 .826087 , 1 5.652 1 74 , 2 3. 47 82 6 1 a n d31 .304348, etc. These could then beconveded to 1 turn + 1 .826087, 2 turns +3.652174, 3 turns + 5.478261 and 5 turns+ 1 .304348, etc. Finally they could besimplified 1 turn + 1.83, 2 turns + 3.65, ,.3turns + 5.48 and 5 turns + 1 .30, etc. thenused to set up each position as accuratelya s i s p o s s i b I e . T h i s wo u I d a vo i d a naccumulating error and probably beacceptable where a high degree ofaccuracy is not being aimed at. If the platewere used via a worm/worm wheel, theimprovement in accuracy this provideswould be a distinct advantage.

A Com puter MethodIf you, or a friend, have access to acomputer equipped with a CAD programthere is another method that may proveuseful. Placing any number of holes on aPCD using a CAD program is both easyand fast. Place a small circie forthe dividingplate centre plus just one on the PCD thenasking the program to repeat this round thecircle the number of times required and theresult will appear almost immediately.

Print this out and fix it to the platealready prepared. Centre punch througheach small circle, also that in the centre,remove the print and examine result lookingfor any punch marks which are obviouslymisplaced . Make any adjustmentsnecessary and use a centre drill to markeach position, again inspect. The ring ofholes can then be drilled. Being very quickcompared to working to X/Y co-ordinates itis an ideal method for Iarge numbers of

7. Photo of the dividing plate print ot/f.

divisions. Photo 6 shows a plate having125 divisions being used which was madethis way. Photo 7 shows the computerprintout. Making the circles on the printoutsmali, say 1 mm diameter, will help toensure that the centre punch marks aremade accurately.

W hiIst fast, the system does haveIimitations, mainly accuracy. The computerdata is of course extremely accurate butmay not be maintained at the printout stage.Having tried the method with a number ofprinters very small errors in the printers'feed mechanisms result in the PCDsometimes being very slightly oval. Notsurprisingly, a print out using a professionalpen plotter produced a perfect result, atlea st a s f a r a s a v a i I a b I e m e a s u r i n gmethods would show. A cheap dot matrixprinter also did remarkably weli, with inkjets and Iaser printers showing varyingamounts of error, even here no more than1 mm on the PCD.

At worst, the errors in the diameterwould produce onsy minute errors in angularspacing and so would be perfectlyadequate providing the radius error of thePCD could be accommodated in themechanics. lf using a conventional detentits plunger would not engage reliably dueto the varying radius. Photo 6 shows howthis was overcome using a heavy gauge,Spring wire detent that would cope withSideways errors whilst still holding the platein terms of rotation. If the plate was to beused frequently on a normal dividing headWith plunger type detent, the plate couldbe used to make a second plate - the holesOn this would then be on a constant radius.

An interesting feature was that the wirehaving a slight taper on its end the resultwas totally backlash free, almost impossiblewith a conventional detent.

Incidentally the ptate was used to slit asmall disk 125 times to make an electronicpulse unit for use with a digital readout foran eight TPl leadscrew.

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C A 1) ? i I h T O d T F 0 lk 1 2 5DIVISION OIVIZIhG FLATE

Made on the Iathe's faceplateFor a simple plate, using the mandrelmounted gear as described at the stad ofthis chapter would be an obvious choice.For more complex numbers, mount a disconto the face plate and using a suitablydivided paper strip round the outer edge ofthe faceplate will enable the disc to bemarked for making a dividing plate. Thepositions can be established using anautomatic centre punch mounted on the tops l id e , o r a s m a l I d ri l l i ng s p i n d l e . T h i sprocess should make a dividing plateaccurate enough for most applications,

55

&

8. Driving dog forbetween centreswork, togetherwith driver (on theye#l stlpplied withthe dividing head.

The published drawing should give aIl thedetails necessary for manufacture.

Rotary tablesMaking rotary tables in the home workshopis not really in keeping with the title of thischapter, ''simple dividing devices'', but isincluded as it is the most appropriate placein view of only a paragraph being required.

A number of suppliers to the homeworkshop provide designs and kits ofmaterials for making workshop equipment,rotary tables being one such item. Photo 9shows a typical 1O0 mm table that has beenmade this way, Iarger sizes are alsoavailable. lf you Iike making workshopaccessories then a rotary table would makean interesting project. None, to myknowledge include facilities for mountingdivision plates but designing this in shouldnot be unduly difficult.

The design for a basic dividing head isthe subject of the next chapter. WhiIst basic,it will be sufficiently adaptable to meet theneeds of many workshop owners.

9. A 100 mm home made rolary table. Castings for these are avallable from a numberof suppliers and y'r? other sizes.

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especially if used via a worm/wormwheel,rather than direct. See Photo 4 Chapter 3.

Taking the need for 53 divisions, asmentioned earlier in the chapter. If using a15O mm diameter faceplate and markedwith 53 divisions on its periphery it will resultin divisions of 8.89 mm wide, so a fairdegree of accuracy should be achievable.

A Between Centres driving dogN ot h a v i n g b e e n a b I e to 1 o ca te acommercial driving dog suitable for usewhen dividing between centres, I amincluding details of the item 1 have mademyself. As described in Chapter 3 (seePhotos 12 and 13) the dog needs to befirmly held by the driving device on the headitself. To cope with differing workpiecediameters a flat plate is used for the drivenportion of the dog, it is atso drilled andtapped off centre so that it can be rotatedto extend the range even further, seeassembiy drawing. Photo 8 shows thedriver, supplied with the dividing head, onthe Ieft, and the driving dog on the right.

56

BETW EEN CENTRESDRIVING DOG

57

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C hapter 7

S ho p -m ade B asic D ivid ing

HeadFor many workshop owners the dividinghead featured in this chapter will be moret h a n a d e q u ate f o r t h e i r d i v i d i n grequirements. lt does though rely on a setof Iathe changewheels being available asit uses these to provide the divisions. Using

a single gear, Photo 1, will provide manyof the more usual divisions namely 2,3, 4,5, 6, 7, 8, 9, 1O, 11, 12, 13, 14, 15, 2O, 25,3O, 35, 4O, 45, 50, 55, 6O, 65, 70, and 75using the most common set of gears, 20 to75 by 5's. W ith a forked detent, Photo 2,

58

1. The singlegear version ofthe dividlhg head.(indexer)

16, 18, 22, 24, 26, 28, 8O, 9O, 100, 110,120, 130, 14O and 15O are also possible.

The range is fudher extended by theaddition of a pair of gears as illustrated inPhoto 3. This, essentially the same asadding a worm and wormwheel betweerdividing plate and the dividing head spindle.There is though one fundamentaldifference, a worm/ worm wheelconfiguration will always have a ratio to one,typically 40 : 1 , 60 : 1 , etc. A pair of spurgears may though have a more complexratio, for example, gears of 45 and 20 willhave a ratio of 9 : 4.

Considering the range of gears above,but only one of each, around 6OO differentcombinations will be possible. This basedon, any one of the gears being used as thedividing wheel. and as the driven. Also,replicating the situation when using a worm/wormwheel, that is input runs faster thanthe output, the driver wheel must always

3. The three-gear version.

59

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be smaller than the driven.W h i 1 st t h e a r ra n g e m e n t w i I I g i v e

divisions of up to 1050, double this if aforked detent is used there is considerableduplication and very many gaps, Iarge atthe higher numbers. On the basis thathigher numbers are unlikely to be required,the table for this setup in Chapter 11 givesaI1 possible values up to 100 that are notobtainable with a single gear. The table,having been produaed with a computerprogram I have developed, covers aIIdivisions mathematically possible. ln somecases the head may need adapting to makesome combinations possible. Typically, withthe base plate fitted as seen in Photos 1and 3 there is a Iimit to the size of dividinggearthat can be fitted. The base is mountedusing 4 screws on a square formation thatp e rm i ts i t to b e rota te d 9 O d e g re e sremoving the restriction. In this positionhowever it may not be easy to mount on aMyford Series Seven type bed. In any casesome readers may wish to use the table inconnection with a dividing head of their owndesign.

An interesting and useful feature ofthese numbers is that they, with only twoexceptions, are achieved stepping fromgear t00th to gear t00th. There is thereforeno need to move across more than onet00th avoiding the complication that thisbrings,

Three possible higher numbers thatmay find a use are also included', these are125, 2OO and 360. In the case of 200 theworkpiece rotates twice and for 360, seventimes, see Chapter 4 for an explanation.

From a dividing aspect there really isno difficulty created by the workpiecerotating more than once and if a gear isbeing made it should not present a difficulty.

60

If though a dial is being made, probably withthree Iine Iengths, ten's, five's and units,great care in the preplanning and the actualcalibration will be required to ensure theIine Iengths are made in the correctpositions. Probably the easiest way will beto make aII lines initially of equal Iength.then marking the position of the five's andten's with different coloured pencils. Theworkpiece can then be rotated, again usingthe dividing head, and the appropriate lineslengthened.

Manufacturelt is not my intention to go deepiy into themanufacturing process as to do this for theshop made items would expand the size ofthe book beyond what is acceptable. It isalso probable that the home workshop userwho has arrived at the need to use adividing head will have fairly well masteredthe processes necessary to make this item.Should you though feel a need for greaterhelp than this chapter provides, you mayconsider obtaining the following additionalbooks in the Workshop Practice Series.Number 34, d'Lathework - A CompleteCourse'' and number 35 ''Milling - AComplete Course''. Construction of thedividing head in this chapter is covered indetail in number 35.

The Body Part 1Photo 4 shows the 44mm diameter boresfor the sleeve bearing being made. Justvisible in the photograph are three supportpieces mounted on the machine table.Providing the initial bore is central in thewidth (5Omm) of the material, the suppodpieces will enable the part to be turned overand bored without the need for furthermeasurement. A high degree of accuracy

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Fit the bearings using a two-part resinadhesive having made the bearing outerdiameter about O.O5mm Iess than the boreinto which it fits to allow space for a film ofadhesive. Set up and bore to final diameteras shown in Photo 5, boring through bothbearings at one pass to ensure alignment.Pay particular attention to clearancebetween boring head, workpiece andclamps, etc.

Slitting the body is straight forward,

Photos 6 and 7 showing the setups.However, depending on the diameter of thesaw the setup in Photo 7 may not fullycomplete the slit. In this case it will benecessary to complete it with a pad saw, ora piece of hack saw blade, pad wrapped inc10th to provide a safe handle.

Spindle Part 12First, make a plug gauge to accuratelyestablish the diameter of the bore in thebearing, This will give you the dimensionfor turning the spindle bearing surface that

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will need to be made using a Ieft hand knifetool, making it impossible to use the spindleitself to test its fit.

The essential requirement for thespindle is concentricity of the four mainsurfaces the gear mounting, bearing,chuck mounting and the internal Morsetaper. This can only be easily achieved ifthese are made without removing the partfrom the chuck. To do this, machine thegear mounting, bearing surface and chuckmounting whilst supported by the tailstockcentre. Then, rflmove the centre, positionfixed steady, re-engage centre, set steadyarms, remove centre, bore and make thetaper.

Remaining partsThe remaining parts should not present aproblem for the majority of workshopowners but should you be at the Iearnerstage then the books mentioned will be of

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help.The drawings do not indicate a method

for coupling the two linked gears used onthe three gear version as it is assumed thatthe pads used on the lathe for a similarrequirement will be used, or an identicalset made for the purpose. Also in thisrespect, the drawings assume gears havinga 5/8in bore and 3/8in width , somedimensions may need changing if the gearsto be used di#er from this.

through 18O degrees and re-engage. Thereshould be no perceptible rotation of thedividing head spindle. If there is, then file avery Iittle from the appropriate detentlocating face and test again, repeat asnecessary, Carry out a similar sequence,this time with the inner faces of the fork.Ot h e r t h a n t h a t , a s s e m b I y i sstraightforward.

In the next chapter a much moreadvanced dividing head is detailed, yetagain being made from stock materials iswell within the ability of the majority of homeworkshop owners. Being a much moreadvanced design, making it should providea real degree of satisfaction.

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DIVIDING HEAD - MULTIPLE GEAR DIVIDING

69

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G hapter 8

A n A dvanced Design DividingHead

The dividing head featured here is muchmore advanced than that in the previouschapter, providing th ree methods ofestablishing the divisions:1. Directly off a gear mounted on thedividing head spindle.2. Directly of'f a division plate mounted onthe dividing head spindle.3. Interposing a worm and worm wheelbetween the dividing plate and spindle.

T h e s e a re b a s ed o n t h e s a m eassembly so the constructor can chooseto make any or alI of the arrangementsusing the one main frame, Photo 1. Therewould though be Iittie point in constructingmethod one only as that in the previouschapter is easier to make and moreadaptable having the additional gear train.When making the head employing methodthree, the method one system, (needingOnly two simple additional items), is wellworth providing for its ease of use withSimple numbers, 3, 4, 5, 6, etc.

The plate on the Ieft hand side of theassembly (Part 3) can be swung into anyposition and in Photo 2 has been fitted witha simple detent mechanism and moved intoan easy to operate position. The rows oftapped holes and the slot in the detent

carrier (Par1 41) enable the arrangementto co pe w i t h a w i d e ra n g e of g e a rdiameters. ln Photo 3 a division plate hasbeen fitted and a detent assembly mourtedoff the arm using the two Sower holes. Thedetent assembly has a slotted Iower armenabling it to function with (different divisionplate hole circle diameters).

Photo 4 displays the reai reason forestablishing the design, the inclusion of aworm and wormwheel. Unlike commercialdividing heads, and probably mostpublished designs for home workshopconstruction, the design is not Iimited to asingle worm/worm wheel ratio. Using 20 DPgears the assembly will cope with a gearup to 65 teeth, Iimited by the gear hittingthe rear of the division plate. The holes inthe end plate will though provide sufhcientadjustment for gears up to 75 teeth andcould be accommodated by increasing the65mm dimension for Part 8 to 80mm andthe Iength of the spindle (27) accordingly.

Chapter 11 includes tables for the threecommon dividing head and rotary tableworm/worm wheel ratios 4O, 60 and 90:1 ,and fitted with 18 different division platehole numbers which appear to be thestandard, The tables will cover for the1

. The dividing head's basic assembly.

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DIVIDING HEAD MAIN ASSEMBLY @ Q

dividing head fitted with both 40 and 60t00th wheels. This still Ieaves gear sizes of30, 35, 45, 50, 55, 65, 70, and 75 that willprovide additional divisions. However, themajority of the divisions possible with thesewill also be possible using either a 40 or 60t00th gear and will be covered by the Iistingfor these. There are though a few that canonly be achieved using another gear,typically with a 35 t00th gear, divisions of77, 91 and 133 are available but not withthe 4O, 60 and 90:1 ratio dividing heads.

I have run my computer program foreach one of the standard changewheel

sizes and the 18 division plate numbers andattempted to extricate from the Iistsproduced, those divisions that can only beachieved with this multi-ratio dividing head.This is also included in Chapter 11 thoughl cannot guarantee that l have not missedan entry or two having had to do thismanually.

As designed division plates up tollomm can be accommodated and as themounting arrangement can be rotated intoany position there is actually no Iimit indiameter. The Iimit is as a result of theIength of the ''detent arm carrier'' (54) and

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W ORM AND GEAR ATTACHMENT

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GEARAND DETENTATTACHMENT

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2. With only the addition of a simpledetent assembly dividing using theIathe's changewheels /'s possible.

ManufactureMaterialsThe drawings are not specific regardingmaterial specifications but the following wiilbe ideal, being easy to machine, Rounditems - 230M07 and rectangular parts -3. Direct dividing using a division plateand detent assembly added for thepurpose.

the ''index fingers'' (29 and 31 ) both of whictcan easily be increased in length when150mm diameter plates could also be usedThe unit in the photos is being used withdividing plates made from sheet steel.These punched plates are made oncomputer controlled machines and are,

even though very economically priced, veryaccurate. They are 3mm thick but thedesign should cope with plates up to 6mmthick. It would though be tidier to increasethe 14 x 1mm thread on Pad 8 to 15mmIong and the 79mm dimension on Part 27to 82mm. Some modification, perhaps abush, may be, may be needed for differingbore diameters. lncidentally, being punchedplates the holes go through whist thecommerciai thick plates have holes that areblind, surely Iess easy to keep them clean.

The design is based on being used witha 3 l4in centre height Myford Series SevenIathe to enable it to be used with the Iathe'staidstock for between centres work. Forother centre heights the appropriated i m e n s i o n s ca n e a s i i y b e c h a n g e d .mounting arrangements may also needchanging. In practice, between centreswork on the lathe is Iikely to be of limited, ifany, use in many workshops in which casethe user may decide to Ieave the design aspublished, its real home being on the millingmachine.

c70M20 (preferred) or 08OA15. 230M07 isfree-cutting and is also available in someuare bar Sizes.sq

Main assem blyvake the end plates (2) to drawing, exceptfor hole B that should only be 4Ommdiameter. Assemble together with items 5,10, 11 and 12, and using iteml3 mount ontothe lathe as shown in Photo 5, The boringbar is lightly gripped in the three-jaw chuck,just suficiently to allow light cuts to be takenbut also permitting the tailstock to feed thebar through the end plate to machine thebore. Do not use the tailstock to feed theboring bar thl'ough both plates at one passbut do one plate at a time. However, stillleave tbeir bores a little undersize, sayminus 0.5mm.

Having bored both ends adjust theboring bar for a final cut, doing first oneplate then Ioosening the chuck moving thebar further into it and then making a finalcut on the other plate. Absolute accuracyis not crucial as the bearings can be turned

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DIVIDING PLATE AND DETENTATTACHM ENT O

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FRONT BEARING 9. REAR BEARING 1.

to fit the bore. The procedure wifl though first bearing. Machine the outer diametersensure both plates are bored to the same and both end faces to dimension, doing thissize, at centre height and parallel to the using Ieft and right had knife tools andunit's base. without removing the part from tbe mandrel.Bearings - Parts 1 and 9 This process ensuring that end faces arePlace one piece of cast iron in the three- square, and the outer diameters concentric,jaw chuck, face the end and make the bore with the bore. Repeat for the other bearing.a little undersize, say minus O.5mm . Slit, make recess and drill and tap M6.Reverse the part in the chuck and face the Positioning the hole for tapping is easilyother end Ieaving it about 1mm Ionger than done as illustrated in Photo 6 using thedrawing. Repeat for the second bearing. bush detailed in SKI.

Leave the second par't in the chuck and Spindle - Part 8finally bore to size. With the tool still set at Mount a Iength of material in the threejawthat diameter, return the first bearing and chuck supporting the outer end with thebore through at one pass ensuring as a tailstock centre. Skim a short Iength of theresult that both are the same size. This is outer diameter for supporting with a fixedessential as both are to be machined on steady. Remove the centre, position fixedthe same taper stub mandrel. steady, refit centre, set steady arms,

Make a taper stub mandrel and fit the remove centre and make the 14 x 1mm

77

E

6. Using a bush to position the hole fortapping in the bearings.7. Setting the division plate carrier (2% to3.5 degrees to suit the helix angle of the

thread, also drill and tap M8.Fit an M8 hex head screw and hold this

in the three-jaw again supporting the outerend with a tailstock centre. Check that theturned portion next to the chuck is runninqreasonably true, if not use the four jawchuck. In this case file two flats on opposingcorners of the hexagon head to take thefour jaws. The remainder of the processfollows closely that for the spindle in theprevious chapter.Division plate carrierThis part needs careful planning. Howevermaking the part as per stage 1 on thedrawings, then creating the 3.5 degreeangle, (first one side then the other) andfinally the two slots as per stage 2 theprocess should be relatively easy. Photo 7shows the part being set up for machiningthe first side at 3.5 degrees.Index fingers parts 29 and 31Cut two pieces of 3mm brass, a Iittleoversize, and mark out the position of the18mm hole. Set up on the Iathe faceplateand bore the hole. Follow by boring to

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g$2 0 D P G E' A R , o R o T H f' R F> . - ( ; H 1 4 ! - - - ' 'j j n n o T y . 1 o F FT O s tl 1 T c ! . A R h v h I t h ;# 1 h . g ko . . . so r o xt - - ..:q0 .-j o-.,u zs -.-. s----- ., ..-; '--, k -''' - -,-- - -,-.Av/kltkuur, oTF4( hywls?E u uo z s !' ,: !!! !! (.)sri:cu. sL I:;uT . 'a a (' -.

clT./. 1 o r. F. . e c-j (;o vv E. k4) c.-j UATL . 1 o uiu o 1( D Syr Eku ,k T u 1 0 x z (: r s ! o R :, o F. F. .$ 'v I -a s r s E L . -$1 or h .

-

jta).t:t: s e-u , - ... , o .-s...

s- x.- zs.-% #' -$&- .+4-.av' v IE.l L 'z lo N s E.c I 10 N tb T 84 R E A D 1A A jy.h A

'

.a A , >:ï-J ' ' g ï u I ua s ! F . !u A r L . 2 17 A F i 1! qz &. ... 8 : Q r Y 1 q) F F .R .-. E)

. -Y . : *. .Y. WO RM S P I N D L E 27 .k ' 6) t, DE E ê?.x: :

yjj 5 Ma ai *- J ià - - - V .......4 y. s o g u s j y r A a- ..j = Y

j1 . li q ., ..j j u , -j us .. ,. . .$ x- ycKd A î L . H R A s s u a T u B R h s 6 -.i -Q T Y ' 1, 1 0 F g

' (tl C(1 D T Y o C1 + - - - ' 1 2 *

79

....à.II 1âs kz

r

13-1 128 12 @ * %

B t j 5 j g g j , y.---j7 k- - co e

.- . (y;cl tyyj-i M V i- - Li T t

- i5 d i o . u l u :) s T E E L.- z) o h .>- 'r- - oTy . ! o F' F' .' 2 5 '

..j5 a S pl A P E E N D T O S LJ I T G E A R B E I N GU S E D . T H E FO R K E D E N D P E R D l T S35

q 8 yyjr (njgyjqjjy 1r- FkOTATrO 9o.TO LOCATE YN ONE TOOTH AbH () LEI S I Z E S . 8 B . 4 . 1w E LL AS E) ETW E E N TW O T E E T F1 .

Qo Cj T H I S D o u B L E S T H E N tl kl B E R O F% A T L . 3 5 X 2 5 S T E E L. D I V1 S I O N S O B T A I N E D W I T H AQ T Y . 1 C F F . G I V E N G E A R

.

DETENT CARRIER 41. DETENT 40.

1 C)h'- o k iE s ! g F s; .-1 k. a. R. 4 8u

<-..- '1' k)/ s d.- r'-' -' ., 04.

''ATSIU/.D slEl' u. i- '''V.!- L , - - - -- -

' ''V..j.u lz -

., u,y. ..t,g... ,- j ...k,,j. .-tg-

31/7 I F ' Q 2 E S l Z F A . 6 . 1 (5 ggju A T L . 2 () X 3 K1 I L D S T E E L . 1 O F F .

s a .-1 p.o20

DETENT ARM 55. DETENT ARM CARRIER 54.

J 1 u- - - - - o4 2 2. ----- - A g--y g'or-V p ti - zaa -Q'

:5 o , yjy n . yr pu. q gIA. udun srs-Lu. ' f.9> --y1t.). , 1, . --4 aRING DRILLING BusH 1,.)s1 ' k ,9 1 2.zo ,BEA

MOLL SIZFS A 1 X 1 D 2 OFF.h. Js x 12 jLr;.SK12 5 kd I L D S T E i: L. () TY .

:5 kg u E) I A . &$ A T L . jj 2 () I AI LD S i L E L .

j ay yy)z e,v . o,, DETENT ARM PACKING 56.-k 2-s DIVIDING PLATE

DRILLING JIG SK2

80

2 9 8 .58 A -# à---1

-i -- ------11 :2 - - - - L - - 11- n --! I

$1 m m , )yplTcyl

I IL ' 1.12

65 161

50

g - --* -)- - .T1ùsk--

....1-k -- ,,PA RT V 1 EW Z

STAGE 1 STAGE 2kà A T L . 4 5 X 3 0 1 I LD S T E E L . Q T Y .

A . 3 m m d i o . P l N P R O J E C T I O N . k A Y R E Q U I R E F LA T S E E2 S P 1 N D LE P A R T 8 .

cI œ U .cxl 5 . 5II

Z

DIVISION PLATE CARRIER 26.

38mm diameter and 1.6mm deep. Repeatfor second part, Mark out outlines and cutroughly to size, then carefully file to profile.The 38mm diameter counterbore giving theoutline of the par't in that area.Division plate nut Part 28This is a straightforward item to make but,when assembled, must clamp the fingersSo that they can be moved, but only withsome resistance. lf easy to move then theymay move whilst traversing the detent fromOne hole to another. To achieve the requiredaction, dish the frontfinger to give the effect

of a disc spring. Form this by clamping thefinger in the vice, backed by a piece of softwood and with a piece of 22mm diametersteel placed centrally overthe hole. Tightenthe vice very slightly to form a dish justsufficient to provide adequate friction.

The remaining pads should not presentany problem. W hen assembled you will bein possession of a quality dividing head,very robust, and able to provide moredivisions that a commercial semi universald ivid i ng head . You will also h ave thesatisfaction of having made the item.

81

. . .... k 11

7

C hapter 9 2. The device .x?mounted on the .h*S CCOSS SIlCe '* 1 'Iê? l .

i

, . 1 h.,,.y . . , .jy .t

: t jo ) îi, . (y )(,jo . yy ' y .rk .. . j y . t ) . , ... . ç ... t )y .. .r! yt '

. ,t . . .

,.. . qtl . . , ,.- a e l n l n: .1 rk Fr qtyjyj; ( .!:.t, .y k.asr..vo.jjyusyrrrj

. lqxlv. ., :< ,,4pt 1 ! . 1: / 7! &tj F.;y ; ... ..

'1 'i lt;)j ! l-ti i)2'î' ' '' - ' -- ;- - .. . .kL- .- '- -- - -. ' '''.. . .- -- - ... .. . . '1 ' ''' '

, ); ,, . jjtu). ,j)) iyëk .. pj;The item in this chapter is not used for k, , p

. dividing and as such is out of place in this' book. It is though a Iining tool for engraving ;. '

? ' ( '' ' ' ' ï; g 2)9 ! b jjt ;) ï kt l , l if ' ''..' n ;: 'I'%EiE (' dials and therefore used where dividing is ., -,.,,, ..., . ,:,.,..,,,,t))i)J' tik#'.?'- ' '

... ; ( y(( . jk ; .very much a part of the task being carriec! r .r. 7 , ..; '' ' z : î. J 'out. Also to my knowledge it is not an item ''''!! ,;. jyr jr

i that is available commercially and has y ïr. .)

,f . .therefore to be made in the workshop. ,,,Ej , '

The purpose of the tool, Photo 1, is tc' .

enable Iines on a dial to be made to setIengths and automatically in the order .$ ; . ' y

,. , c :' yrequired. Typicallyforan imperial Ieadscrew ., . .1' . ...,su... .. , , . t.dial the sequence would be, one long ' . ' '

jj ,?pr,,. . . (tens), four short (units), one medium Iength c 't.,,.,,(# -.. ,. yjx p,, ,,,.. .. )..!..:'j)'':' l ,> ing as ;kt,$;k:).,q;

,ë..,;.

' ' tt . . y-t..zy;.rptlil#ltllt' ê #).)jt;''). (fives) and four shod (units), repeat ,,,.t j') r èj ...:.7) t rl ' / 1 j ; );î )?)j. ' lp- klr i t$ 1 is .. . ... . . -.--k... .'-. .... . . . ;, jj 7èî. .. .-. 'agjlflhltlll,-: ) ) ).)yl;tl., -... r' (E2, (:4 t.l i r- (E5, 4:j . -. - - .'f .. j .q yjjt.yjâgikt ë -èitC'lpt;

, a'iae differences in Iine Iengths are 0.025 mm making it very close to 0.001''. Iengths by observing its Ieadscrew dial4lt.lpz. :- trolled by the stop disc (4) this is not This would need a ratchet having 8 teeth readings and having to count the numberjj#? cOn

adjustable but being such a simple item, and giving, one Iong (0.1 mm) three short of Iines made of each Iength. Photo 3others can easily be made as required. The (0.025 mm), one Iong (0.1 mm) and three shows it being used in conjunction with thesequence is controlled by a ratchet wheel short (0,025 mm). basic assembly of the dividing head in the''' (12) and pawl (11). The ratchet wheel as Tjne unit would normally be used on previous chapter mounted on the lathe'sdrawn has ten teeth Iimiting repeat the Iathes cross slide with the top slide bed

.

2 5 or 10 Should another removed as seen in Photo 2. The position Ideally the cutting tool should besequences to , .

sequence be required a second ratchet of the Iathe's saddle would be set and nominally at the Iathes centre height, it may

wheel would have to be fitted, W hilst locked to give the line Iengths required and therefore be necessary to change the 40J The Lining device, note the recesses lb internal, changing the wheel is not a Iarge the cross slide set to give the depth of cut

. mm and 72 mm dimensions of the angle

82 83

7x z. -z oo ut 1 .

O + . - . * u --r7 76TO LIUIT DRAWING SIZE,HANDLE ''7'' IS SHOWN 30 50 20 1 5 25 E) 1 .8s H O RT E R T HA N S 1 Z E 1 1 1 1 () --j$76G t V Eq N O N P A RT D R AW 1 N G . S E C T I O N A A 7

C I 1 1 1. . m . ; : , c

1 2 sa -T '!- j.s, I , . . .

, a r? jj --j q o j ! r g s,- - .1 - (.y. yj o ujys .A

y)- o A. 1 () E). u4. 4 og-g', c. 9 wIDE suo'r, @ j,o ,s ',,' yjwyu. gsj y j (; syyyjyu oyoszo oyy. g oy-r..o: 1 () ; , s w.-.

58L - - @ - - - - . . - - - - - - - - - - @ D j.-.......41 9 jj () y gj . jk g: g) o c gj y o g 5 y yj j c K w I y H I T Eg u qA

) ' ' F' I T y E () i x p t. A c ,(E A s A R E s U L. T u A c H i N 1 N G: l l 1 l L A-')- T ; E k-rh t! T H E F L A T O N 1 T E k1 1 A T T H E S A hd E 1 I H E .-c o - @ --r;. o @ 6: c zc SLIDE BODY 2

H O L E S .7 8 9 H 1 H (; A ' V 4 .C

. 8 W 1 D E:. .4. +. -+HARDWARE

H 1 . 4 m m D I A . STE E L BA LL AN D S H ORT COM P R E SS I O N S P R 1 N G . ' I 2H 2 . M 4 X 1 O S O C K E T H E A D C A P S C R E ZW 1 O F F . hz A T L . 3 0 XH 5 . M J X 6 ! 0. C- K- E- T. j j U- j j C.w j E. W. . 2. 0,. r F. . j j hj j hj m .r n n j Q T Y . ) C) F F -l- -$H 4 . M 4 X 5 ti L) U K. L I ki tx tl r b t, x t f? . l t/ r r . u . n : n - . v v - j j RH 5 . k! 4 X 6 S O C K E T G R U B SC R E Wj 1 O F F . ! jH6. u4 x 1 o socxEy HEAD cAp cREw. 8 opy. ASSEMBLY ANGLE BASE 9.

.

., . j %%Y' . - . 4. . -.

. .. . . )... .. 8!; (:) ë!; (2. '

....k jj....: 6j 7 6.k!. given have been established to suit a 7 tpo ltyj$.et, M ford Series Seven , jjouEs . 4.w.

SDca y . s y Czt (;: grp. ë! oy-g..Lè1 y. . ..

.. r.... .;. .t tjyj-,11 . . s

'

;

'

. . . tj ;

'

'

'

. . !'

)j(7. -1 ë)t ill. '-ytjjikir-' r )-- yt.tj,y y itryrtjyyjyyj. g- ).j r . -)#jp(yy' -y -jt -t-jtyyyè.iyyy' ).tt,-t# ;, lk-jkyjù jttjjtljjk-lj ,?jf),l iy.j,-kë t ;- ''.' lù ' -h'i(,- I,I.I!II ClislL Ir-'I1 1k.-II hlq: CIE!IL dt::)i tlk: 1k.-Il Ir-' d!!z:q (::à ': -,r. . .1 (::, s-. E:. . ' 'lt' )t! ù'ttt . s ;, t... . ' once more I will only comment on those,jt ,-u,,,,.

jl J yjs jyuj jt jym m y N g k g g g R j g g y j g.r..,s. .. r%.. Rfy =:> t j manufactu re that Warrant it Tne *, ,, ,,..,,. ,,.,, aspec s o .)

. .. i, ))),j;t..t 7 ., . main consideration when making the', ': IjE jE f7 j,qq jl ljjj )))r: ' J rl - / r r, .,) - -- ) - -'- ' . - - ' .' ' . .. . - ' 7 i. :. . .E' '' jt),))t.l)j.tg,q.. .,r ,, various parts is to ensure that the sl ideljlity.

-jjg- :. . . .- ' r; : ;q -. - t'','-'':. -')?.r.y ,, tj ;,. '(, ( -)t j k) ( ti,j)),)#tt-.'t''-;pyt. rj:)- - ' ''lri , . :

' . . . ' - 'iy' p p. . 'tl'''itls.' ' '''' moves without perceptible shake. This is cut out on the slide. This ensures that anyt. .

'#, . ' the reason for the flat on the second side slight sideways movement at the end of the. . Ct 5 ' Li 1 1'' '' ' '' '

)) ''' . ' ' 3. Being used to Of the slide (1 ) ensuring that the slide mates pawl does not result in it catching on theIt ; . . .

- engrave a milling with slide body (2) on its sides. Otherwise, slide and preventing it engaging with themachine any clearance between their two diameters ratchet wheel,

. peadscrew dial. Would result in the pads mating only in the The slide assemblyThl's is using the bottom of the semi circular portion of the Place a Iength of 22 mm diameter steel in

$,/2 ., . dividing head from Slide body. the chuck, suppod by the tailstock centre. .. ..() r.. . ,: . lqk ji''''' L'' 7't ious Another feature for which the reason and reduce to 20 mm checking to ensure-=.., iw'? . ,,. .ë yj). lqj, lhe prevrt. .u,j. qr, ;( .t .l. . j j atjjust tjae'., . ',lk..'tl ) ..., 7 chapterï S n0t obvious is the 1 2 mm x 1 mm deep that it is being turned paralle .

8584

. ' . 11. . . . .. âL .IIw .uo

ol1 t

'

.L L = --I

1 .1

2 3 4 H1 H H3 5 6

H4

d!!::!!h dtrEErzzh.d::)- .....' ..,,'''i'

I 1 $ , I .k.''' .;k 4 ' 4k

rBoring the ends

of the slide body(2)

tailstock set over if required.Next, cut a Iength of material for the

slide body and machine it to Iength, thethickness being Ieft at 16 mm at this stage,machine the recess and slot C also holesA, B .

Carefuliy mark both ends of the bodywith the centre position of the 10 mm radiusand centre punch. Mount the slide body or:the face plate using an angie plate, or t)Keats angle plate, as in Photo 4, and usinf?a centre finder to accurately position thte

!@ . : )'

. :

'

t! ,'

.. 1) g '' ' . '.

. .., ( y. , i j. . r $4.. .? jw. . . . . .jtt rùn ,(, .

.. j ok. .... . lr... ,'Jr . .. . . j .; j , ..

.jlj t , j.)j. j); ); j k. '.p t r! :(,....;j : j Lâ. . . .. j .. .? yyq ;)y . t fjyyj

. t .

.. '.'qt )1p jkjjy y y j ar.. : u:y.

E ?r 3... :., rj ty.jj k y , j... . $.. . .- n 'pkjtgtjj j yjj)Cj ,s4 !r

') é)' !

. ., ., . .. . qjj j.. . î, ..<...r '' . '' -'

. j . y . . :' .

. .. 5 uj//jng ttte

. '' ' ' second flat on the

sjwe ())

A -. .. c ' (u3 (--.. - .-...

- - .t. y:@L- u . .

x '- .

zo ts t- -c1 ..w-r- --! , - t . ,k 1 ? öb . ..z'-- I 73 '-j t-tp.-k j j T- .2 0 1 1 .Z. .. . , jj r y y6 RA D -.+- -.j - .j 44 t) .-- b

>'' tz - '-T;'

'A ;' (:77 ju-x =.. '' '. x v px .) 1 !., ... . .. ' ' . . . .. . yh i O L L ES ' -

N O T E G . 'A . 8 . 2 B .1

. D R i L L H C) L E B A F 1 : R A % G L k1 Ei L Y A hk DW H 1 L Ek T F I 7 '= L D T (3 T H r L A T H F % t) A %- 1 C E N T R F H F I C F 1 T . V A 1 2 . 5 T F1 I 0 K-r O E N S U R L H C L E I G A

-. (3 T Y . 1 O F F .2

. LE FT f-l A N L) k-l (3 LE (. I % F () R LJ tq Eq F o Rkq o t- () $ hk t7 T hq r p A R J' T o G F' T H E( R w I T . . PAW L j jl T E k! 2 W H L

. N kl A C H 1 N I N G T H E. I %' (3 83 A R T S *G t qd LJ L I A N E C U f.-a ( %r h1 C) T U G ;- f3 F C) R F ' I hi A LA S S 62 K? 83 t . Y .

- : 1 7 j- : j, z58 A T L . 2 0 D I A .1 O F F . 1. 'Q T Y . 1 CD O 'Z

S L I D E 1 . Az ir -YI . : 23

TCHET W HEEL STOP PIN 5.- j',* - ' , ..j(., .--- vf;? i......-11 ::42 .-2)-' --2. - y ,$ y, ,,'. v o -1 C) I h .

.5 ---,1 po; ; -'r , .% .-.y ,? . .1 1 c . pl .$-J vL),: (-... g u ,L z k4 ' ' D i ) 1 >'k . S T i E L

1 j-...y cxy s. ) Ty' I o :p Oj Vj s c c A R R I E R 3 .% co (Dr--'i HANDLE ï.kkt

- - - - -

s s's %' n ou t - - - - -uATk-. cx -. j.-.2 rj g)oI Av j . %. T 8 E 1 (.....--. .. .. .. . X 9 . 1 D I A . .z' -* ro '-o-ry. .. .-..-- -7 t

. 1 ;? s (tp tt ' qkf AT t . 1 2 L) @ A . A N D 8 !q T E Eè L ;' 5t3 k! () 7 .

- '

Q l Y . 1 (D U r' .

This wouldpartfor boring. Cut two small pieces of steeland drill to fit across holes B at either end.These allow each end to be bored 20 mmdiameter as a continuous rather than anintermittent cut. Bore the slide recess in oneend as shown in the photograph to be aClose fit on the slide. Remove, reverse andrepeat the operation on the other end.Flowever, if you have a suitable angle plate,rather than the Keats, and a Iong boringtool it would be better to machine both ends

without removing the part.guarantee alignment.

Next mill the first flat on the slide - theone that passes along the whole Iength ofthe pad. It is essential that this is the samedepth along the Iength or else the part willget wider along its Iength causing it to beIoose at one end of its movement. W ith thisin mind, hold the part in a vice and witheach end supported by precision parallels.Take a very Iight cut of about 0.05 mm deep

. ' . ; .. J

A- - - i

- .j y. :I1: 1 1 :$ ---@ 6 F-4 ',1 5

T H l S G I k E S L 1 N E L L N G T H S+ 2 A N D + 4 . K1 A K E( E X T R hD I % C S F O R O J ri E R L I N EL j (1 G T H S .

STOP DISC 4.

18 8 16K-O V- z t-t

: - (x;

B

Q Q

K4 A T L . 1 6 D I A . S T E Eq L 2 J O % O 7 .Q T Y q C) F F .

SLIDE OPERATING POST 6.

H. I N G E P I N 8 .

$-n--a-1. o4-; -T

1 8$4 A T L .6 E) I A . S T E E L 2 3 O Kd O 7Q T Y 1 0 F F .

$q

along the Iength to check if aIl is well. Anyerror will be obvious in the varying width ofthe flat produced. ,. yl ë; $ jr r j 44 :j y .g .j .Drill and counterbore holes C, and use ihlf'- , ,

. ' ' .., . .. . . ?

these to fix the part to the slide body for è 'machining the second flat. Again support r

lthe ends on parallels and machine both ,( l .

slide and body to achieve the 1 5 mm , ty. ' '' ' ?' r' ., ër : yy .y ,r . ;)) ) ;) yt q.. 't. , . .. , ' .. 't jtrl pp,hly, ' ïr '' ' ., i'' ; k: yjjy yyy ' t). jj )j, y tk 3. k r j; ..,. .,. yj.j y jjyyyy jjy4.

j .s .

: ' -.... .y. j,(.... ' )jy jjj yjjjjytk . j .. 5 . .

'

y . tj yjj jj jjj.g . yzyyjjjry.The rem aining parts , '' ' : ,. , .)p.)q. , ,jd.t.'#i't. '.k.y. t Ltvb,. - . .

. ' - . - .. k-') y- ...... . . :)2 j' l .. !.k,..' k) j.: ,.. ..,... .ki. #. , . rr , k, ,tr. 4 p . . iThese are aIl straight forward and need no ' ,) ,. .' ''.k u .?jg .) , , ,.,, ' êk'' ' , : - ' ,,); ,, y' E ) ë' ' s t rt , ; . .?: @ ë t ;! ; . . .. .y . . ,,, ... s .. .comment other than to say the ratchet will tj

j, 1 'r .) ayltjr ' ;/''' ,,: j'; v; ) . j. . ..;. ' #( 0..1;:9 c' E)'s j ) k . t ' ' . . C '. .. . ? 1$ .(be a good first item to produce using either k

.? ( ) . ; j yj , yy ,j. ' )y. jyl : j , ' < j jof th e d i v i d i n g h e ad s i n th e p rev i o u s ,) ( .-, , y,,. -. . #' .k . ,; . ... r. t;k j j . . . . tt . ,,..y ) lrrjjjjjjjjjyj. 5 s,.. . ..chapters, see Photo 6. The part was first ' , .tr)y. , k . . ,..' ? r 'k: ll# -' . ' . wjk l ''' r)l' ppr '' '' - '-- r . i, . tturned on the Iathe, then moved to the : t Et , ) .jiy' ' l -; . . -)r )) ) 'k -' .. '; .-. - -- . ,.milling machine still in the three jaw chuck 74; (ir : .,i'' .. , .,)?...

'

); ''. ... .....and the ratchet machined as shown. It was '' .k.Jo.? , . ... (y y ,: .. ..then returned to the Iathe and paded off *,?').from the stub in the chuck. Finally held on ;?) 7;

( r; j - . .the smaller d iameter and the parted face , a't''ljljjytjlgtj, . j;,

finally machined to achieve the required 'thickness for the ratchet. 6. Machining an eight t00th ratchet wheel.

89

, I I

.. .... .1.. . .. , . kk.... . :

88

C hapter 10

Prim e N um bers

The reader may ask, what are primenumbers and what is their relevance to thesubject of this book?

Taking prime numbers first. These arenumbers which are only divisible by 1 anditself', typically, 1 , 2, 3, 5, 7, 11, 13, and onup to infinity. There are therefore very manyand even a very advanced mathematicianwill be unable to recognise beyond valuesof a hundred or so. For this reasor tablesof prime numbers are an essentialrequirement when dealing with suchnum bers.

Prim e factorsThese are those prime numbers that whenmultiplied together give the number beingconsidered. For exampie, prime factors of1O5 are 3, 5, and 7.

3x5x7 = 1O5The method of arriving at these from a Iistof prime numbers is as follows1 . Is the number even? No therefore startusing the tables,2. Look up 105 and the smallest factor is 3.3. Divide by 3 to give 35.4. Look up 35 and the smallest factor is 5.5. Divide by 5 to give 7.

90

41 will give 47 also found to be a prime having a worm/worm wheel ratio of 40:1umber. The prime factors therefore 41x49 then for 1 turn at the output 40x49 holes onnw 1927. Obviously a time consuming task the plate will be passed, that is 1960. Asithout the aid of the tables. explained in earlier chapters any numberwUnfortunately though, space Iimitations that divides exactly into this will be a

in this book restrict the table to 2000. To possible division. To easily arrive at valuesminimise the task of finding prime numbers possible if will be necessary to find its primebove this a Iist of prime numbers up to numbers as explained above. Dividing bya10 0O0 is also included. This will avoid 2, 2, 2, 5, 7, 7 giving 980, 490, 245, 49, 7,looking for the prime factors of a number 1 .which is in itself a prime number, typically, The result will be 2, 2, 2, 5, 7, 7. which4933. are of course, numbers of holes and must

be divided into 1960 to determine theNum bers greater than 2000 division possible. Ignoring the higher

6. Look up 7 which is found to be a primq First take note that no number in the range numbers possible as they are unlikely tonumber. 2000 to 10000 has a prif'ne factol greater have a practical use, the more useful values7. The prime factors are therefore 3, 5 ancl than 97

, that is 24 possibilities. In this range are typically.Z' therefore take the following approach: 1960/2x7=140

First, if even, divide by 2, if not try 3, 5, 1960/2x2x5=98Prime factors of an even 7 jl etc

. until the lowest prime factor is 1960/2x2x7=70num ber found. Having found this, divide the number 1960/5x7=56For this find the prime factors of 132. by this value and in most cases the result 1960/7x7=401. Being an even number the smallest will then be below 2000 and the table can 1960/2x5x7=28factor is 2. then be used. lf not, repeat after first 1 have also ignored the lower numbers,2. Divide 132 by 2 to give 66, again an even checking to see that it is not a prime such as 1960/2x2x5x7 = 14 as these arenumber. number, bound to be achievable by an easier route.3. Divide 66 by 2 to give 33, The procedure is unlikely to be as time As already mentioned the prime factors4. 33 is an odd number consuming as may first be thought as every relate to the number of holes traversed,5. Look up 33 and the smallest factor is 3 third number is divisible by three, every fifth therefore for 28 divisions the number of6. Divide 33 by 3 to give 11 . number by five, every seventh number by holes traversed will be 2x5x7 = 7O. As the7. Look up 11 which is found to be a prime Seven and so on. As a result most numbers division plate being used has a ring of 49number. have a Iow first prime factor. holes. this will be achieved with 1 turn plus8. The prime factors are therefore 2, 2, 7 21 holes.and 11 . W hat use are Prime num bers? Some readers will l am sure have

2x2x3x11 = 132 How then will this be of use when dividing? noticed that the prime factors 2, 2, 2, 5, 7Both these examples are simple and prime Well, you may have acquired a second and 7 are in fact the prime factors of thefactors could easily be established without hand dividing head without its manual, or two initial values, 40 ( 2x2x2x5 ) and 49 (the aid tables. purchased an additionai plate not on your 7x7 ). However, l have presented the

However, consider finding the factors manual's list, in these cases you will have explanation in this form as when workingof 1927. This, itwill be found, is not divisible to resod to calculations. with thethree geardividing head in Chapterby 3, 5, 7, 11, 13, nor 17, etc. Its Iowest Consider a division plate having a ring 7 the ratio may not be a simple one, sayprime factor is in fact 41. Dividing 1927 by With 49 holes. If this is used with a head 60:1, but with gears of 45 and 35 the ratio

9 1

i .p . .1 1 u ad

will be 9:7. In this situation it will be easierto work with the number of holes passedwhich in some cases will be with more thanone revolution of the workpiece, asexplained in Chapter 4 Example 3.

Having provided the Iist of primenumbers l have decided to include brieflysome details on another and mored e m a n d i n g u se f o r t h e m . T h i s i sestablishing gear sizes for complex ratios,it may of course create a need to use yourdividing facilities for making a specific sizegear.

Designing gear chainsA typical use for prime factor tables is inthe design of gear chains requiring complexratios, such as when determining changewheel combinations for cutting Metricthreads on a Iathe with an imperialIeadscrew, and visa versa. Also whencutting worm wheels which similarly requirecompsex ratios.

ExampleIf requiring to cut a thread with a pitch

of lmm or a Iathe having an 8 TPI Ieadscrewthe lathe's mandrel will have to rotate 25,4times whilst the leadscrew rotates 8 times.This therefore requires a ratio of 25.4 : 8.

Expressing this as a fraction we get:8 1

=

25.4 .314960629Accepting that an exact ratio will not bepossible, this can be simplified to

1

. 3 1 5As decimals are not appropriate to fractionsthis must be written as

1000 'rhis gives a TPl and 5, 30 by 10 and 35 by 5 to give40x50x75 4Ox1 x 75

31 5 8 x = 25.3968254 8 AThat is multiplying both top and bottom by 30x35x45 3X 7 X 451000. pitch in millimetres is very close atFactorising both 1000 and 315, using the 25.4 simplified givingtables, we get = 1.OOO125mm

2x2x2x5x5x5 25.3968254 40 x 75At 25 pitches this is a total error of plus 8 x = 25.3968254

3x3x5x7 0.0031 25 mm or if you are imperially 21 x 45Cancelling out one 5 we get inclined O.O00123in in practice a negligible This will be easier to set up using only two

2x2x2x5x5 amount, drivers and two driven but requires a 21This can be simplified by dividing 50 by 10 t00th gear that witl be special for most

3x3x7 changewheel sets.Ignoring the fact that gears cannot be madewith so few teeth, we still have a problemas there are 5 driven gears but only 3drivers. If we multiply 2x2 and 2x5 we get -.#drivers and 3 driven as follows

4x10x5

3x3x7Multiplying each number by 10 will givepractical gear sizes and being in 10's areIikely to be available with the Iathe. We get

40x100x5O

30x30x70A 1OO t00th gear is unlikely to be availableso reducing this to 50 and the 70 to 35 willretain the ratio.

40x50x50

30x30x35The combination now requires two 30 acdtwo 50 t00th gears, but, increasing one ofeach by a factor of 1.5 they become 45 ard75 $00th gears, again retaining the ratio.The resulting gear chain becomes:

40x75x50

30x45x35

92

.I5

œ N X œ =

X X & & X N X A X Xko (D. X X LO a. C9 X C ko C9 C)X r = v W

c. X N to X = m co ko s. co= = m (nO a. to X C) = O & a. X P' X X Q. U<tor- c. r< a. X r< a. X m ko g) c) g) a. c; a. a. g) m z) g) o.m D m % ok m m

to (D. n. (9 LD X X v- X O &. >. O a. ko O X a. X to >' X(D = C< = = = X-(D D. X X kn œ (nm D =

CD N X X X X a. tD X X Q. X LO &. O >' = X a. C) X X to X X =m = v' m ko

A & X X A X X N & % œ O D œ m x N= D

= X r œ X X X X X N X = A X X X O X X X œ N O N œ =m > = v- kD

% D. CL X F) m a. (9 >. u7 (n co a. co z) N co a. œ (n a. a. ro a. ko co a.m & (9 mX a. ko X a. C1 X tD a. X r< Q. X X Q. X Q. tO f9 Q, N' X LO Q. X mm v- = to

X c. b. C9 u3 (9 X a. = tn a. pw n. g) ko = (n co N g) m a.= D (N cu ro = = a-

a. v' X X r< X &. & X Q. &. C9 LO &. X Q. &. C9 ?< U> X a. to C9 X =tD= = = x c. = C X CL Xv- = cg v-

a. X LD a. O N Q. X &. X X Q. to X a. &. X LD m X Q. Q. X &. Q.= m a. a. Qn co ot

(9 a. to X a. X X to X X Q. X X U< Q. X Q. LO O Q. Uw O T) Q. X(Q. œ & to N X a. a. cg m a. & c) u7 co g) co co ko a. coD

= cu = cu

= (9 27 N. C m O LO >. * = C9 tO U> C1 m X ko >. C) = X LO U< C23 LO tO tD LO (D (D (D (D (D N. N U< U< r< X X X X X 03 C C) C1 C) r' X tO U- C = X Y) N C m X ko >. C) = (9 to N c)to T) ko ko ko (D (D (D (D c co a) co co co c) c) c) cp c)

m =v- oc o. >. co to a. co a. = c7 >. a. co co to c7 a. >. c9 to a. co a. (9 (n a. c7 == = = = = cq v- = CY EL m X Q. (9 O œ LO O C5 >' X to = X G. CL X O >' O C) to O Q.X = = v- x = = xr . cu.4 v-m > &c D

. c9 = uo c9 a. a. O u7 = c9 a. a. (9 a. a. cg >. Lo g) a. ut c9 un >. (9 o. a a. ko fo m s. c) co a. a(D D = = C< X O= D (9 = %O

X D X N X X X C X X N X X X X X X X X N Qm C<<m

& & X X A X X X X X X X X X X N X X X X œ = G & > r & œ > & o m & N x x œ mX & = m K œ m

m=

N X X = X X X X N X X O & O N X X X X X = X X A Y X & œ & N œ= = m = a m<>

X X X = G X X X O X X X X X X W N X A X X = X & m XQ2

= s. co œ a. <= &-m =m C

c c X O A X O Q œ G X X A N O N X X X O O X A X X œ O A X OX X = U O M X

D =tn = ko co a. k = 0. X a. to X a. = X u7 X O = a. O b' Q. X = LO O N N X u7 = X

m m D = = = m X

> =oa. a. co a. œ co a. u7 co a. a. (n ko œ co a. a. (n a. >. * CD ZY U- >' X * X O Q' to C9 œ L' CO tO O O Q' c' CO >' Xa. a. œ a. co 1 = . = . m

m D r N c m c r N œ = X A N C = X & N c= X r N c m o c N c = X c N c = & œ > c % % vv m m m m œ m a œ m O O X D X + %œ œ m œ x O O O X O % % % % %

94 95

. ... 1. . u :u2

= c) =>. co *

tn v- = ch (J: h- Oco J) (D c) >. = co

c) (r) = (n >. = >. (9 (D = = ?< == hu * = (o = * b. = ry (7: >. =>. >. >. tn = v- = c) >. >. 0) = tn F) ?< = tn mœ c) >. >. co to co = >. (D = c) œ co = = N == = >. = v- c) (n = >. J) >. = m m = = m >. (n tn = v- >. tn (9 co= co c) c) >. (D co c) z) >. = >. (D (D = co >. >. = co co (D (D = œ ots. = = tn c) tn ot tn m tn e) (D = >. = = c) = ct >. (n tn >. = m = c) (n>. >. * o) % (D to co to >. >. to to N (D >. (D >. >. * u7 = * œ) * co >. (0= v- = >. tn >. = c) = >. e) e) tn = = = tn O >. c) N N c) = = tn c) >. *-

>. xr to (D (o to cp >. >. ço (D fo œ >. % to œ % >. to >. toto >. >. co % Lo u7= >. c9 v- v- = >. c) tn >. tn = N tn = = tn v- >. v- r- = tn m >. >. c) >. co (mu7 fo >. co % c9 to xr % (D ko to to % co (D b. (o u7 (o to to % tn >. % (D u7 N %c) tn m = >. >. (9 c9 5) v- >. e) >. s. tn tn v- >. = c) tn = >. = = m cp F) >. s.tn œ) to ko r9 tw T) % co * % % % tD >. to (D ro % ko * T) (9 % to % * to (D cotn >. >. s. = = = = >. O (n tn cn = c) e) c) O tn c c) c) c) c9 >. >. m = tn (ncq % tn % e) tN to % (M to % tn ol (N to to to O O % F) G1 (N tn to (n % % to e7v. cn tn tn = J) >. >. = = >. = = tn = v- tn c) c) >. >. N = v- v- = cn s. = Ncu = c9 tn v- = % tn Cq e) tn tn G1 cu ko to to = tN % œ cq = tn ko cu tn tu % m= c9 = co >. >. = >. e) s. = = >. >. c) >. >. = >. >. (D v- co = O (n = O c) o:

c % = v N œ œ = m % % O D œ = = œ = œ O m œ œ œ mm m x œ mc N > c & X & = N O = O m m N & O O X = O O v & N N N N & Nc c œ c v & O = & W = m m > œ œ = c œ = m & = o = = & > W cO = c O > = 0 = = 0 N v O m = = > = X N = X N N = N O X N m& c & c & & œ & & o c c c c œ W c & & & & & & c m c c c = &c = Cu (n % ko œ >. * 0) & = œ O % u3 (D N * 0) c = tN tn % to (D >. * c)ko u7 to u7 tn ko tD u7 to 43 (D (D œ c e (D (D œ (D œ >. >. >. N >' >. >. >. >. >.

. s.

>. = (M = c) c) c *'>. C)= (p Cp 0) c) co c)

= O O tn N = c9 c9 tn co oj ro 05s. rw0) = c) = 0) co = (m co c) O

= >. (m (D v- O (9 s. &- co s.* (D œ * = >. * J) cz >. (0 v- m X U< * O (X U-

C) C) CD * C) f< * *>. X >. = >. (p >. J) >. m o) (o* ; c) c) X c) œ V ; V 5) >. ;: (p c c) >. O r< f< = O N' v' b' * b' >' C) *- O= * J) * * (D = * * C1 (D >' C XO F) = (n 17 >. >. = (9 = 0) N tn = c) co m tn m c) co c)* >. * = X >. (D = X = 1Z c) D N c) (D (D >. to cn = >. c) c 0) = tn m = = O b. = O m X >. N. v-* (M b. * * >' (D (D * * CD (D r< * N'v. = c) >. N = >. >. = v 0) m m c m o) e) o) m s. >. c tn tn (n c >.* >. c N >. = b. (D >. N. >. c) s. u7 cn u7 >. N * c ko u7 a) co >. co to >. cj (7) c to s. m = (M = O v- s. m v- v- = tn* h- c * b. ?< (D to C u7 ?< * P- (D (D * tD ?<C m >. = O c) = e) = Gt N >. c) >. c) >. = c) >. >. m >. c >. v- rw o >. px< to c >. >. >. >. * (D (D c (D u3 % œ to >. œ >. % to >. z) ot œ (o (o co to m m co s. s. e) c) (n c) v- c m s. m c) c) c) >. s.* b. (D * (D lD (D ko % t< % (D U< U- W) * (D kD (DO (9 = N >. >. O = >. O = = >. tn >. p- = >. (n (n c) o) co = co m s. tn c v-œ œ) u7 ko œ to (D % u7 r fo œ u7 % to % u7 c e % % ko % = œ fo to co co to c) s

. o s. m m e) s. c) on co >. s. c) s. p- e) s. v- c)(D (D % b. to % (D % O tO % LD u7 * O X * & tD %(9 tn X m c) = c) = = s. = c) (n m tn = c9 m tn m N N m (n s. c) v- = >. toto % % to to u7 u7 % to u7 % (D to (9 to % % c to tn tu ko % >. to % ko to s. % cj m s. 0) s. c s. x- s. co m m m tn ro x- x- ot g) m

(M = = N >' = >. v C9 (9 = >' v- = v- (M N = = = v- (9 = tn = N o = pv to ID X (D * X V * O CD * (D V * O Y' O V O *O % c9 % % % u7 e) % ko % fo to cu œ g) e) tn to cq cu to (n fo to % % u7 % co e) s. g) ro g) s. . s. m . uj s. c) .. .. s. cj e) e) m* >. >' = = O >' = >' C >. X c) O >. O = O >. O c) c) c >. >. m tn tn c3 tD * O X * X V O O to W O O V O * W V O Ocu tn c9 % % % % G1 tn O c7 c (N cu ko (n co (n % cu m co cu u7 % cq < tn (J co e) co s. s. m m (o ct o; ojc) F) v- O v- >. Ct = = =P< = = C >' = C9 * O N. X N = = 03 = X >. O = O O c) = m cp cp c = m O m O LO O X CV O QN V = O txl O W O W O B1 WC< O Cq X * O tn = (9 eq œ * tY v- % œ œ (N O = = tn m % % m co cu tn co

>. b. = @) c) v- b. = C) O = U- = X * X Ot O U< C9hw = X X O = = O @) b. C = >. (9 (9 >. >. 0) O >. s. = s. c) co >. >. (n s. c) = v' QN Gl Gl (N œ v- = C9 v- (N tNl Gl v- C) v' O = Glm m = & N D m = m > > œ = = m m m m œ m o m m m œ m m a m m> m œ N O X X X N O G c & O O m X m = Om X N = N = N m O c m c c N o N * c = = O N m N = O m m o c m m = = œ v m m o œ o & & m v œ m m m om m c m m œ m m o c m m o c m m m c m m o m m o œ m a m m oc m œ m c v O N O X = X O D X m m O O mX = X & m O & N = O = & O m N = N = X N m m m N c N O & m O o o o m w o o o o m o o o m o m o m o o& = c & = c c & c & & & c & o = & & & & c m c m c o o o o c o o œ o % o c N o c & = m X % c c N c o

D = m X % C X N X O c = œ X % c c N X c & m œ O % o c N œ c œ c o œ o o o o o o c c c c c o c c c ca œ œ œ œ m m œ œ a X X X X O X O D X X % % % % % % % % % %

9796

, i.u.u

t

, .'

ne turn of the input will rotate the output those additional values possible, quotingO

division, and is obviously achievable for each value the gear ratio required to1* onewith any one of the eighteen division plate achieve it. They are aII relatively highvalues. Twenty will similarly be arrived at numbers and mostly numbers of little use.with two full turns per division. Forthe same One hundred and twenty-five is though onreason 20, 30 and 60 are omitted from table the list that will be useful f0r that dial

a jes two and 30, 45 and 90 from table three, required for an 8 TPI Iead screw.Of greater significance for theColum n Headings workshop owner who constructs theThe column headings D, P, T and H relate dividing head is that in addition to the aboveto the following extra divisions he or she will get 23 fudherD. Division achieved divisions (51 being the lowest) using thep. Number of holes on the division plate 60 :1 ratio that are not available with the 40

ln the final section of this book a number of dividing head, Iists six set-ups for 24 to be used : 1 ratio, being by far the most commontables are included to assist in arriving at a divisions. T. Number of full turns at the input commercially available dividing head.suitable set up for the project in hand, H. The number of additional holes to beHaving purchased a new dividing head a Based on Division Plate sizes trak' ersed after the number of full Lurns, if Three Gear Dividing Headtable of possible divisions will be included The tables can of course only cover a range any. The dividing head in chapter 7 uses eitherWith it that will be fine in most of division plate numbers and are based R. Ratio (gear sizelApplies to table 4 only. a single gear or additionally a pair of gearscircumstances. However, a second hand on those commonly supplied with a smaller Providing the same function as a worm andhead may have parted company from its head. These are 15, 16' 17, 18, 19, 2O, 21 , W orm/W ormW heel ratios wormwheel. The ratio will though be Iower,manual and should you make one yourself, 23, 27, 29, 31, 33, 37, 39, 41, 43, 47 and Tables 1, 2 and 3 are for the commonly typically gears of 60 and 20 having a ratiotypically that in chapter 8, arriving at a 49. available ratios of 40 : 1 , 60 : 1 and 90 : 1. of 3 : 1, or complex, gears of 65 and 45suitabie set up would necessitate recourse However, the head for home workshop having a ratio of 13 : 9.to calculation. You may have noticed that I Possible divisions not included construction in chapter 8 can have 9do not refer to ''the suitable set up'' but to To limit the size of the tables for publication additional ratios, for example, 35 : 1 using No table is provided for the single gear''a suitable set up'' this is because in many some values have been omitted.

Values the 35 t00th changewheel. Publishing 9 as in this case the results should beCases there is more than one method of below 20 are not included as they can easily Other Iists in full is obviously impractical and obvious. Two examples being, a fody t00tharriving at the same result, often many be arrived at by observation and some in any case most of the possible divisions gear providing 2, 4, 5, 8, 10 and 2O, a thirty-methods. simple mathematics. Obviously, values of With these will also be achievable with the five t00th gear 5 and 7. Again the table is

The manual supplied with a 15and above will use division plates having 40 : 1 and 60 : 1 ratios Iisted in tables one Iimited to 16 to 200 plus 36O but alsocommercial head understandably quotes that number of holes, say for 17 use the and tWO. Ieaving out divisions that can easily bejust one set up for each value on the basis plate with 17 holes, the holes traversed Forthat reason, table four includes only achieved with a single gear.that the supplied division plates will remain being equal to the head's ratio, say 40 forwith the head. However, we aII know that a 40:1 head. Typically for other values, forthis so often is not the case and one plate 7 divisions the 21 hole plate would be themay go missing. For many values this will obvious choice. Values above 200, 36Onot be a problem as the required division excluded, have been omitted on the basiswill be achievable using another plate. For of their Iimited application.this reason the published tables include Observing table one, for a 40 : 1 head,every set-up that provides an achievable it will be seen that no values are given fordivision, typically, table one, for a 40 : 1 either 20 or 40 divisions, This is because

98

....n

l :i1' ! r) :1. DIVISIONS POSSIBLE USING A 40:1 g. nIVISIONS POSSIBLE USING A 60:1DIVIDING HEAD PIVIDING HEAD

D P T H:1 :1 2 18 45 18 l 6 84 49 0 35 t35 t8 Q 8:1 49 2 42 45 21 1 7 85 17 0 12 I35 27 0 12D P T H,2 33 2 24 45 27 I 9 86 43 0 30 I38 23 0 1021 21 I 19 41 41 0 40 75 15 0 8 I32 33 0 10:3 23 2 14 45 33 l 11 87 29 0 20 I40 21 0 922 33 I 27 42 21 0 20 76 19 0 10 I35 27 0 8:4 16 2 * 45 39 I 13 90 15 0 10 I40 49 0 2123 23 I 17 43 43 0 40 78 39 0 20 I36 17 0 5

24 15 1 10 44 33 0 30 80 16 0 8 I40 21 0 6:4 18 2 9 46 23 l 7 90 18 0 12 l4l 47 0 2024 18 1 12 45 18 0 16 80 18 0 9 I40 49 0 1414 20 2 10 47 47 I 13 90 21 0 14 I45 29 0 12

24 21 I 14 45 27 0 24 80 20 0 10 I44 18 0 5 25 15 2 6 48 16 l 4 90 27 0 18 I47 49 0 2024 11 l 18 46 23 Q 20 :2 41 Q 2Q l45 29 Q 8 25 20 2 8 48 20 l 5 90 33 0 22 I48 37 Q 1524 33 I 22 47 47 0 40 84 21 0 10 I48 37 0 10 16 39 2 12 49 49 l 11 90 39 0 26 I50 15 0 624 39 1 26 48 18 0 15 85 17 0 8 I50 15 0 425 15 I 9 49 49 0 40 86 43 0 20 I52 19 0 5 17 18 2 # 50 15 3 92 23 0 15 l50 20 0 8

27 27 2 6 50 20 4 93 31 0 20 l55 31 0 1225 20 I 12 50 15 0 12 88 33 0 15 I55 31 0 8 18 21 l 3 51 17 3 94 47 0 30 156 39 0 1526 39 I 21 50 20 0 16 90 18 0 8 I56 39 0 10 28 49 2 7 52 39 6 95 19 0 12 I60 16 0 627 27 I 13 52 39 0 30 90 27 0 12 I60 16 0 4 29 29 2 2 54 18 2 96 16 0 10 I62 27 0 1028 21 I 9 54 27 0 2û 92 23 0 60 l60 2û û 528 49 I 21 55 33 0 14 94 47 0 20 I64 4$ Q IQ 31 31 I 19 54 27 l 3 98 49 0 3û l64 41 û 15

31 16 I 14 55 33 I 3 99 33 0 20 l65 33 0 1229 29 I 11 56 21 0 15 95 19 0 8 I65 33 0 8 33 33 I 17 57 19 l I I00 15 0 9 I70 17 0 630 15 I 5 56 49 0 35 98 49 0 20 I68 21 0 5 34 17 I 13 58 29 l I I00 20 0 12 172 43 0 1530 18 l 6 58 29 0 20 I00 15 0 6 I70 17 0 4 35 21 I 15 62 31 0 30 102 17 0 10 I74 19 0 1030 21 1 7 60 15 0 10 I00 20 0 8 I72 43 0 1030 27 I 9 60 18 0 12 104 39 0 15 I80 18 0 4 35 49 I 35 63 21 0 20 I05 21 0 12 l80 15 0 5

36 15 I 10 64 IE 0 15 I05 49 0 28 l80 18 0 630 33 I 11 60 21 0 14 I05 21 0 8 I80 27 0 6 36 18 l 12 65 39 0 36 I08 18 0 10 l80 21 0 730 39 I 13 60 27 0 18 I08 27 0 10 184 23 0 5 36 :1 l $4 66 33 û 3: l08 17 ; 15 lgc 17 p 931 31 I 9 60 33 0 22 II0 33 0 12 185 37 0 8 36 17 j $8 68 j7 û js jj: 33 û j8 I8û 33 o jj32 16 I 4 60 39 0 26 II5 23 0 8 188 47 0 1032 20 I 5 62 31 0 20 I16 29 0 10 I90 19 0 4 34 33 j a; 69 za c ac jj1 j7 c zc jac yq c jy

36 39 l 26 70 21 0 18 lI4 19 0 10 I85 27 0 1233 33 I 7 64 16 0 10 l20 15 0 5 I95 39 0 8 37 37 I ,2 7c 49 c 4: us a3 c

j; j:6 31 c jc34 17 I 3 65 39 0 24 I20 18 0 6 196 49 0 10 38 19 j jj 72 jy c js jj6 z: c jj jgg 47 ; js35 21 l

3 66 33 0 20 I2Q 21 0 7 200 15 û 3 39 ): j aj 74 j7 c yc jjy ;q c :c jq; jq ; 635 49 I 7 68 17 0 10 I20 27 0 9 200 20 0 4

36 18 l 2 70 21 0 12 I20 33 0 11 360 18 0 2 4: 16 j a ps js ; ja y,g j6 ; a jNa j6 ; s

:0 18 l 9 75 20 0 16 l20 18 0 9 I95 39 0 1236 17 1 3 70 49 0 28 I20 39 0 13 360 17 0 3 4c :c j jc

ys j, c js jz; ac c j; jN: #q c js37 37 l 3 72 18 0 10 l24 31 0 10 41 4j j jq yg y, g yg jzj 4j ; zg j,, yy g jg38 19 1 j 71 27 o ls 1a

8 16 p s 4, zj j q y; jy ; jz jz# yj ; js z;; z, ; o39 39 l I 74 37 0 20 I30 39 0 12

42 49 1 71 80 20 0 15 I26 21 0 10 360 18 0 3:3 43 I 17 81 27 0 20 I29 43 0 2066 33 I 12 82 41 0 30 I30 39 0 18XS 15 1 5 84 21 0 15 I32 33 0 15

1 01

.. .I..I.k

t' ..c .-.102

I

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i I DIVISIONS POSSIBLE W ITH A THREE GEAR. I ..

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' 48 1 30 25 4049 1 35 50 70

' 52 1 20 25 65

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, I NOTES! 1 USES A STEP UP RATIO GEAR 0N' I . 1 I) HEAD SPINDLE SQALLER THAN THE$$

. DRIVER11 2 USE EVERY OTHER TOOTH SPACEI

3 UsE FORKED DETENT AND EVERY; TOOTH ANn SPACEII 4 DIVIDING HEAD OUTPUT ROTATES

' jj I THREE FULL TURNSI Ij1 5 DIVIDING HEAD OUTPUT ROTATESj SEVEN FULL TURNS' j I. ' jI I r

. .1 ' j 104! ; j'', ; F û- F 7