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Chapter 1

un amen a oncep s

D. B. Wallace, Ph.D., P.E.Brad Hembree, Ph.D.

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nemat cs an ynam cs

KinematicsDeals with motion only Position, time, ve ocity, an

acceleration

Deals with forces and resulting motion

, , ,inertiaPosition time velocit andacceleration

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Device to transform ortransmit enerUsually consists of a number

Bodies are usually connectedwith joints

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nemat c agram

Machines drawn in skeleton formIncludes only dimensions relative to the

Joints connecting bodies are indicated

Rigid links have no deformation

Stationary portion of the machine

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nemat c agram xamp e

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ec an sm

Kinematic chainSystem of links (rigid bodies) Connecte wit joints

Or in contact with one another (direct

Mechanism

Single degree of freedom

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ec an sm

Unconstrained kinematic chainMore than one degree of freedomStructure or truss

Less than one degree of freedom

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egrees o ree om n a p ane

Each one has three degrees of freedomHorizontal motionVertical motion

RotationJoints

Removes degrees of freedom

Revo ute pin joints remove 2Prismatic (translational) joints remove 2

Rolling direct contact joints remove 2

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egrees o ree om

DF 3 Nl

1 2 Nr

Np

1 Ndc

1 Nrdc

links revolute prismatic direct_contact rolling_dc

Must have a fixed

TOTAL number of direct contact joints How many of the

direct contact

joints are rolling

NOTE: Ndirect_contact Nrolling_dc

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egree o ree om xamp e

Links: 6

Revolute Joints: 7

13

5

Direct Contact Joints: 0

Rol ling D.C. Jo ints: 0

DF 3 N l 1 2 N r Np 1 N dc 1 N rdc DF = 3(6-1)-2(7+0)-1(0)-1(0) = 15-14-0-0 = 1

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u t p e evo ute o nts1

2

v u = -11

No J oints 1 Joint 2 Jo ints 3 Joints

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DF=3( 6 -1)-2( 5 + 2 )-1( 0 )-1( 0 )DF= 15 - 14 - 0 - 0 = 1

DF=3( 5 -1)-2( 5 + 1 )-1( 0 )-1( 0 )DF= 12 - 12 - 0 - 0 = 0

DF=3( 5 -1)-2( 6 + 0 )-1( 0 )-1( 0 )DF= 12 - 12 - 0 - 0 = 0

DF=3( 4 -1)-2( 3 + 0 )-1( 2 )-1( 1 )= - - - =

DF=3( 5 -1)-2( 4 + 1 )-1( 1 )-1( 0 )DF= 12 - 10 - 1 - 0 = 1

DF=3( 7 -1)-2( 5 + 3 )-1( 2 )-1( 1 )DF= 18 - 16 - 0 - 0 = 2

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nvers ons

Fixing different links in amechanismRelative motion between the links is

not changed T e appearance o t e mec anismmay be quite different

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Slider Crank Mechanism

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pt c ramme

.

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am oup ng

.

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cotc o e

.

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nvers ons o an set er ran

Offset Slider Crank Crank Fixed

Slider Fixed Connecting Rod Fixed

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Offset Slider Crank Crank Fixed

Slider Fixed Connecting Rod Fixed