lecture 3-ch. 1 fundamentals and degrees of freedom
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8/3/2019 Lecture 3-Ch. 1 Fundamentals and Degrees of Freedom
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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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8/3/2019 Lecture 3-Ch. 1 Fundamentals and Degrees of Freedom
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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
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