some elements in engineering design

8/10/2019 SOME ELEMENTS IN ENGINEERING DESIGN

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SOME ELEMENTS IN ENGINEERING DESIGN

Ion PETRESCU,PhD. Eng. Lecturer at TMR, UPB

Victoria PETRESCU,PhD. Eng. Lecturer at GDGI, UPB

ABSTRACT:The paper presents first the MP-3R inverse kinematics solved directly by an

original method. Second one presents the V engine kinematics and dynamics design by an

original method. Third one trate shortly the dynamics design of geared transmission.

Fourth one presents the cams design. Last it presents the Otto Engine Design.

1. The MP-3R Inverse Kinematics

One presents shortly an original method to solve the robot inverse kinematics

exemplified at the 3R-Robots (MP-3R).

The system which must be solved (1.4) has three equations (1.1-1.3) and three

independent parameters ( ) to determine. See the figure 1 and [1].302010 ,,

x1

y1

z0, z1

O1

O0

x0

y0

10

a1

d1

y2

x2

O2

z2

a2

d3

d2

20

A

z3x3

y3

O3Ba3 M

30

M

M

M

z

y

x

203032

2021

1010

=

=

=

Figure 1: The geometry of 3R Robot (MP)

++=

++++=

++=

)3.1(sinsin

)2.1(sincoscossincoscossin

)1.1(coscossincoscossincos

3032021

1030310310202102101

1030310310202102101M

ddaz

dadady

dadadx

M

M(1.4)

We aim to solve the system directly obtaining accurate solutions. At first step one

multiplies the equation (1.1) with 10sin 10cosand the relation (1.2) with , then add the

two resulting relations and one obtains the relation (1.5) with solutions (1.6) for the first

independent parameter 10 .

321010 cossin aayx MM +=+ (1.5)


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+

+++=

+

+++=

22

2

32

22

32

10

22

2

32

22

32

10

)()(sin

)()(cos

MM

MMMM

MM

MMMM

yx

aayxyxaa

yx

aayxxyaa

(1.6)

10cos 10sinNow one multiply the equation (1.1) with and the relation (1.2) with , one

add the two resulting relations and obtains the relation (1.7), which form with (1.3) a new

system (1.8) who generate the last two independent parameters .3020 and

+=

+=+

)3.1(sinsin

)7.1(coscossincos

3032021

30320211010

ddaz

dddyx

M

MM

(1.8)

One use the notations (1.9) and it obtains for the system (1.8) the exactly solutions

(1.10).

=

+

+=

+

+=

3

202130

2

2

2

2

1

22

2

2

2

2

2

2

112

20

2

2

2

2

1

22

2

2

2

2

2

2

121

20

coscos

)(2

44sin

)(2

44cos

d

dC

dCC

kdCdCCCk

dCC

kdCdCCCk

++=

=

+=

2

3

2

2

2

2

2

1

12

110101 sincos

ddCCk

azC

dyxC

M

MM

(1.9) (1.10)

Finally one keeps the three solutions (1.11):

=

+

+=

+

+++=

3

202130

2

2

2

2

1

22

2

2

2

2

2

2

121

20

22

2

32

22

32

10

coscos

)(2

44cos

)()(cos

ddC

dCC

kdCdCCCk

yx

aayxxyaa

MM

MMMM

(1.11)

2. The V Engine Design

One just remembers about an original method to solve the kinematics and dynamics of V

engines. The calculations can be seen in [2] and the issues in [3]. The geometry of V

engine is presented in figure 2.

The V Motors kinematics and dynamics synthesis can be made optimally by the value of

constructive angle ().For this reason, as generally constructive value angle was chosen randomly, after various


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technical requirements constructive or otherwise, inherited or calculated by various factors

(more or less essential), but never got to discuss crucial factor (which takes account of the

intimate physiology of the mechanism) angle that is constructive with his immediate

influence on the overall dynamics of the mechanism, the actual dynamics of the

mechanism with the main engine in the V suffered, the noise and vibration are generally

higher compared with the similar engines in line.This paper aims to make a major contribution to remedy this problem so that the engine

in V can be optimally designed and its dynamic behavior in the operation to become

blameless, higher than that of similar engines in line.

In the picture number 2 one can see the kinematics schema of the V Engine. The crank 1 has a

trigonometric rotation () and actions the connecting-rod 2 which moves the piston 3 along theslide bar B and actions the second connecting-rod 4, which moves the second piston 5 along theslide bar D. There is a constructive angle between the two axes B and D.

+

-

O

B

D

A

C

Fm

FBm

FCmFBm

FB

FCm

FCn

FCn

FD

/2--

/2++-

2006 Florian PETRESCUThe Copyright-Law

Of March, 01, 1989,U.S. Copyright OfficeLibrary of CongressWashington, DC 20559-6000202-707-3000

V Motors Kinematics and Dynamics Synthesis by the Constructive Angle Value ();Forces Distribution, Angles, Elements and Couples (Joints) Positions; a+b=l

1

2

4

3

5

r

l

a

b

/2 /2

BD

||B

Figure 2: The geometry of V engine

The same constructive angle () is formed by the two arms of the connecting-rod 2; firstarm has the length l, and the second (which transmits the movement to the second

connecting-rod 4) has the length a; this length a, add with the length b of the second

connecting-rod 4 must gives the length l of the first connecting-rod. The crank motor forceFmis perpendicular at the crank length r, in A. A part of it (FBm) is transmitted to the first

arm of connecting-rod 2 (along l) towards the first piston 3. Another part of the motor

force, (FCm) is transmitted towards the second piston 5, by (along) the second arm of first

connecting-rod 2 (a).

A percent (of motor force Fm) x is transmitted towards the first piston (element 3) and the

percent y is transmitted towards the second piston (element 5); the sum between x and y is

1 or 100%. The dynamic velocities have the same direction like forces. From the element 2

(first arm) to the first piston (element 3) one transmits the force FB and the dynamic

velocity vBD.

To force the first piston velocity equalises the dynamic value, one introduces a dynamic

coefficient D .BThe second Motor outline can be solved now. In C, FCmand vCmare projected in FCnand


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v . The transmitted force along of the second connecting-rod (FCn Cn) is projected in D on the

D axe in FD. One determines the dynamic coefficient in D, DD. One put the condition tohave a single dynamic coefficient of the mechanism, D=D =DB D. The value of x was

determined from the imposed condition to have a single dynamic coefficient for the

mechanism.

The dynamic analysis made with the presented systems indicates some good values forthe constructive angle (), which allow the motor in V works normally without vibrations,noises and shocks (see the table 1):

Table 1: The alfa angle values in grad

[grad] [grad]

0 8 155 156

12 17 164 167

23 25 173 179

With

indicate in the table 1 one can make V Engine work without vibrations. The valuespresented in the table are not convenient for the motor makers; one can correct them with

the relations presented in [2].

3. Geared Transmissions Design

One just remembers about an original method to solve the kinematics and dynamics of

geared transmissions (see [4], figure 3, and the relation 3.1). In this paper one makes a

brief presentation of an original method to obtain the efficiency of the geared transmissions

in function of the cover grade. With the presented relations one can make the dynamic

synthesis of the geared transmissions having in view increasing the efficiency of gearingmechanisms in work [4].

i

O1

O2

K1

K2

j

A

rb1

rb2

i

j

kl

ri1rj1

rl1

rk1

Fl, vl

Fml, vml Fi, vi

Fmi, vmi

2005 Florian Ion PETRESCU

The Copyright Law

Of March 01, 1989

U.S. Copyrig ht

Library of Congress

Washington , DC 20559-6000

202-707-3000

Figure 3: Four pairs of teeth in contact concomitantly


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)1(2

)12()1(3

21

1

12

1

012122

1

2

0

2

++

=

z

tg

ztg

m (3.1)

4. Cams Design

In the figure 4 one presents shortly four models of cams mechanisms [5].

O

A

r0

s

s

rA

1vr

2vr

12v

r

B

C

D

Fr m

Fr

cFr

F

E

2002 Florian PETRESCU

The Copyright-Law

Of March, 01, 1989

U.S. Copyright Office

Library of Congress

Washington, DC 20559-6000

202-707-3000

0A

A

B

A-

Fn, vn

Fm, vm

Fa, va

Fi, viFn, vn

Fu, v2

B

B0

A0

A

O

x

e

s0

r0

rA

rB

s

n

C

rb

2002 Florian PETRESCU

The Copyright-Law

Of March, 01, 1989


Library of Congress


202-707-3000

a-Cam with plate translated follower b-Cam with translated follower with roll

0

A

A

2

B

Fn, vn

Fm, vmFa, va

Fc, vc

Fn, vn

Fu, v2B

B0

A0

x

rbr0

rA

rB

A

B

OD

0d

b

b

2002 FlorianPETRESCU

The Copyright-Law

Of March, 01, 1989


Library of Congress


202-707-3000

r0

G

B

O D

d

A

A0

B0

H

I

l

b

G0

l.

.

r

Mm

x

1

2

Fm;vm

Fa;va

Fn;vn

2002 FlorianPETRESCU

The Copyright-Law

Of March, 01, 1989


Library of Congress


202-707-3000

c-Cam and rocking follower with roll d-Cam and general plate rocking follower

Figure 4: Cams kinematics and dynamics

The cams design (geometry, efficiency, forces, dynamics) can be followed in the paper[5].

5. Otto Engine Design

In the figure 5 one presents shortly the Otto Engine Design [6].

(c)

2

222 )cos(

1cossin

sin

1)sin(

)sin(sin

l

re

rF

rF

P

P

m

m

c

u

i

+===

=

==

(5.1) (d)

2

222

22

]sin)cos(cos)cos([

)(sin)(sin

l

rerel

rF

rF

P

P

m

m

c

ui

+++=

==

==

(5.2)


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0

0

O

A

B

l

r

e

yB

x

y

P

1

2

3

1

y

0

0

O

AI

BI

l

r

eP

1

2

3

I

I I

y

0

0

O

AII

BII

l

re

P

2

3

II

II

l-r

xx

l+r

II

l

near dead point

distant dead point

a - the crank is in prolonging

with the connecting-rodb - the crank is overlapped

on the connecting-rod

a-The kinematical schema of Otto b-Extremely positions.

0

O

A

B

l

r

e

yB

x

y

P

-

Fm

Fn

F

Fn

Fu

Fc --

0

O

A

Bl

r

e

yB

x

y

P

-

Fm

Fn

F

Fn

Fu

Fr

-

-

c-The forces of Otto-mechanism, when the d-The forces of Otto-mechanism,

piston works like a motor mechanism when piston works like a steam rollerFig. 5.The Otto Engine Design

6. Conclusions

Today industrial machines construction requires new technologies of manufacturingwhich require a permanently renewed fundamental research. The presented elements of

industrial machines (mechanical) design are trying to fit these requirements.

BIBLIOGRAPHY

[1]

Antonescu P.: Mecanisme i manipulatoare, Editura Printech, Bucharest, 2000, p. 103-104.

[2]Petrescu F.I., Petrescu R.V.: V Engine Design, ICGD2009, Vol. Ib, p. 533-536, ISSN1221-5872, Cluj-Napoca, 2009.

[3]Petrescu F.I., Petrescu R.V.: Designul motoarelor n V, Revista IngineriaAutomobilului, Nr. 11, iunie 2009, p. 11-12, ISSN 1842-4074, 2009.

[4]Petrescu R.V., Petrescu F.I.: Geared Transmissions Design, ICGD2009, Vol. Ib, p.541-544, ISSN 1221-5872, Cluj-Napoca, 2009.

[5]Popescu N., Petrescu R.V., Petrescu F.I.: Cam Gear Design, ICGD2009, Vol. Ia, p.

215-220, ISSN 1221-5872, Cluj-Napoca, 2009.[6]Petrescu R.V., Petrescu F.I.: Otto Engines Design, ICGD2009, Vol. Ib, p. 537-540,

ISSN 1221-5872, Cluj-Napoca, 2009.

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