Table Of ContentMechanisms and Machines:
Kinematics, Dynamics, and
Synthesis
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Mechanisms and Machines:
Kinematics, Dynamics, and
Synthesis
MichaelM.Stanišic´
UniversityofNotreDame
• (cid:129) (cid:129) (cid:129) (cid:129) (cid:129) (cid:129) (cid:129)
Australia Brazil Japan Korea Mexico Singapore Spain UnitedKingdom UnitedStates
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MechanismsandMachines:Kinematics, ©2015CengageLearning
Dynamics,andSynthesis
WCN:02-200-203
MichaelM.Staniši´c
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ToLauren,Emily,andOlivia.
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Contents
Preface xi
Acknowledgments xvii
1 Introduction 1
1.1 Joints 2
1.1.1 P Joints 3
1
ThePinJoint 3
TheMultiplePinJoint 4
TheSlidingJoint 5
TheCircularSlider 6
TheRollingJoint 6
1.1.2 P Joints 8
2
TheSlippingJoint 8
1.2 SkeletonDiagrams 9
1.2.1 ExamplesofSkeletonDiagrams 10
1.3 MechanismsandMachines 26
1.4 Gruebler’sCriterionandDegreesofFreedom 28
1.5 Mobility 33
1.6 Grashof’sCriterion 36
1.6.1 CranksandRockers 36
1.6.2 GrashofFourBarMechanisms 37
1.6.3 Non-GrashofFourBarMechanisms 39
1.6.4 Grashof’sCriterionAppliedtoaFourBarKinematic
ChainwithaSlidingContact 41
1.7 Problems 45
2 KinematicAnalysisPartI:VectorLoopMethod 55
2.1 KinematicAnalysisandtheVectorLoopMethod 55
2.2 HintsforChoosingVectors 61
2.2.1 TheStraightSlidingJoint 62
2.2.2 TheCircularSlidingJoint 63
2.2.3 TheStraightPininaSlotJoint 64
2.2.4 ThePininaCircularSlotJoint 65
2.2.5 ExternallyContactingCircularBodies 65
2.2.6 InternallyContactingCircularBodies 66
2.2.7 CircularBodiesPinnedatTheirCenters 66
2.2.8 EvaluatingVectorLoops 67
2.3 Closed-FormSolutionstothePositionEquations 78
vi
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Contents vii
2.4 NumericalSolutionstoPositionEquationsviaNewton’sMethod 80
2.4.1 GraphicallyCheckingtheSolutiontothePositionProblem 82
2.5 TheMotionofPointsofInterest 85
2.6 Problems 87
2.7 ProgrammingProblems 96
ProgrammingProblem1 96
ProgrammingProblem2 97
ProgrammingProblem3 98
2.8 AppendixI:DerivationoftheTangentoftheHalfAngleFormulas 99
(cid:2)
2.9 Appendix II: Matlab Code Used in Example 2.10
DemonstratingNewton’sMethod 100
3 KinematicAnalysisPartII:RollingContacts 103
3.1 ExternallyContactingRollingBodies 104
3.2 InternallyContactingRollingBodies 105
3.3 OneBodywithaFlatSurface 106
3.4 AssemblyConfiguration 108
3.5 Geartrains 114
3.5.1 SimpleGeartrains 116
3.5.2 ATwo-StageSimpleGeartrainwithCompoundGears 119
AManualAutomotiveTransmission 121
3.5.3 PlanetaryGeartrains 125
TheModelTSemiautomaticTransmission 129
ATwo-SpeedAutomaticAutomotiveTransmission 131
AnAutomotiveDifferential 134
TheGearRatioofaDifferential 136
Transaxles 136
Comment 136
3.5.4 HybridGeartrains 136
3.6 Problems 137
3.7 AppendixI:TheInvoluteToothProfile 154
3.7.1 MechanicsReview:RelativeVelocityofTwoPointson
theSameRigidBody 154
GeometricInterpretationforPlanarMotion 155
3.7.2 MeshingTheory 156
TheInvoluteToothProfile 160
3.7.3 PressureAngle 162
3.7.4 Nomenclature 164
4 KinematicAnalysisPartIII:KinematicCoefficients 169
4.1 Time-Based Velocity and Acceleration Analysis of the
FourBarMechanism 169
4.2 KinematicCoefficients 170
4.2.1 NotationUsedfortheKinematicCoefficients 171
4.2.2 UnitsAssociatedwiththeKinematicCoefficients 171
4.2.3 PhysicalMeaningoftheKinematicCoefficients 172
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viii Contents
4.2.4 Use of Kinematic Coefficients in Velocity and
AccelerationAnalysis 173
4.2.5 CheckingtheKinematicCoefficients 175
4.3 FindingDeadPositionsUsingKinematicCoefficients 176
4.4 FindingLimitPositionsUsingKinematicCoefficients 178
4.4.1 TimeRatio 181
4.5 KinematicCoefficientsofPointsofInterest 182
4.6 KinematicCoefficientsofGeartrains 184
4.7 Problems 186
4.8 ProgrammingProblem 191
ProgrammingProblem4 191
5 MachineDynamicsPartI:TheInverseDynamicsProblem 192
5.1 ReviewofPlanarKinetics 192
5.1.1 SummingMomentsaboutanArbitraryPoint 194
5.1.2 NotationinFreeBodyDiagrams 196
SimplificationsinMomentEquations 201
EffectsofGravity 208
5.2 Three-DimensionalAspectsintheForceAnalysisofPlanarMachines 209
5.2.1 SpatialKineticsofaRigidBody;TheNewton–EulerEquations 210
5.2.2 TheNewton–EulerEquationsReducedforaPlanarMotion 211
5.2.3 Summing Moments about an Arbitrary Point for a
PartiallyThree-DimensionalPlanarRigidBodyMotion 213
CompositeBodies 214
ComparisontoPurelyPlanarCase 215
5.2.4 DiscussionoftheFourBarLinkage 215
5.2.5 Equivalence of a Reaction Force and Moment to
TwoReactionForces 219
5.2.6 Three-DimensionalAspectsofPlanarForceAnalysis
inSection5.2 221
DeterminationoftheBearingForces 224
5.3 StaticForceAnalysisandInertiaForceAnalysis 227
5.4 ForceAnalysisofRollingContacts 228
5.5 Problems 234
5.6 AppendixI:KinematicAnalysisforExamplesinSection5.1
(Example5.2)andSection7.2 256
5.7 AppendixII:ComputingtheAccelerationsoftheMassCenters
oftheCompositeShapesinSection5.2.6 258
6 MachineDynamicsPartII:JointFriction 259
6.1 FrictioninaPinJoint 259
6.1.1 ComputingtheDirectionIndicatorDyx foraPinJoint 261
Programming 262
6.2 FrictioninaPin-in-a-SlotJoint 263
6.2.1 ComputingtheDirectionIndicatorDyx foraPin-in-a-SlotJoint 265
SignoftheDirectionIndicatorforaPin-in-a-SlotJoint 268
Programming 268
Copyright 2015 Cengage Learning. All Rights Reserved. May not be copied, scanned, or duplicated, in whole or in part. Due to electronic rights, some third party content may be suppressed from the eBook and/or eChapter(s).
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