Advanced Regression Models with SAS and R

305 Pages·2018·21.077 MB·English

by  Olga Korosteleva

AdvancedAnalyticalDynamics
Thisbookprovidesauniquebridgebetweenthefoundationsofanalyticalmechanicsand
application to multibody dynamical systems. It is intended as a textbook, particularly
wellsuitedforgraduatestudentsseekinganunderstandingofthetheoreticalunderpin-
ningsofanalyticalmechanics,aswellasmoderntaskspaceapproachesforrepresenting
the resulting dynamics that can be exploited for real-world problems in areas such as
biomechanicsandrobotics.
Establishedprinciplesinmechanicsarepresentedinathoroughandmodernway.The
chapters build up from general mathematical foundations to an extensive treatment of
kinematicsandthentoarigoroustreatmentofconservationandvariationalprinciplesin
mechanics.Parallelsaredrawnbetweenthedifferentapproaches,providingthereader
withinsightsthatunifyhisorherunderstandingofanalyticaldynamics.Additionally,a
uniquetreatmentispresentedontaskspacedynamicalformulationsthatmaptraditional
configurationspacerepresentationsintomoreintuitivegeometricspaces.
VincentDeSapioisaresearchscientistatHRLLaboratoriesinMalibu,California.He
hasmorethan40publicationsand16patents(issuedorpending)intheareasofmulti-
body dynamics, robotics, biomechanics, control theory, and human motion synthesis
and simulation. Dr. De Sapio is a senior member of IEEE and a member of ASME
andSigmaXi.HeisafoundingmemberoftheIEEETechnicalCommitteeonHuman
Movement Understanding. He received his Ph.D. and M.S. from Stanford University
andhisB.S.fromRensselaerPolytechnicInstitute,allinmechanicalengineering.
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Thelightshinesinthedarkness,andthedarknesshasnotovercomeit.
John1:5
S.D.G.
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Advanced Analytical Dynamics
Theory and Applications
VINCENT DE SAPIO
HRLLaboratoriesLLC
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Informationonthistitle:www.cambridge.org/9781107179608
DOI:10.1017/9781316832301
©VincentDeSapio2017
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Firstpublished2017
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LibraryofCongressCataloging-in-PublicationData
Names:DeSapio,Vincent,1968–author.
Title:Advancedanalyticaldynamics:theoryandapplications/VincentDe
Sapio(HRLLaboratoriesLLC).
Description:Cambridge,UnitedKingdom;NewYork,NY:CambridgeUniversity
Press,2017.|Includesbibliographicalreferencesandindex.
Identifiers:LCCN2016036860|ISBN9781107179608(hardback;alk.paper)|
ISBN1107179602(hardback;alk.paper)
Subjects:LCSH:Dynamics.|Mechanics,Analytic.
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Contents
ListofIllustrations pagevii
ListofTables xi
Preface xiii
Notation xvii
1 Introduction 1
1.1 HistoricalBackground 1
1.2 DevicesThatIllustratePrinciplesofAnalyticalDynamics 5
1.3 ScopeofThisBook 8
2 MathematicalPreliminaries 10
2.1 LinearSystems 10
2.2 DifferentialGeometry 23
2.3 Optimization 28
2.4 Exercises 31
3 KinematicsofDiscreteSystems 36
3.1 SphericalKinematics 36
3.2 SpatialKinematics 54
3.3 KinematicChains 69
3.4 KinematicConstraintsandDegreesofFreedom 76
3.5 Exercises 77
4 ConservationPrinciples 83
4.1 TheNewton-EulerPrinciple 83
4.2 Exercises 99
5 Zeroth-OrderVariationalPrinciples 101
5.1 VirtualDisplacements 101
5.2 D’Alembert’sPrincipleofVirtualWork 101
5.3 Hamilton’sPrincipleofLeastAction 128
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vi Contents
5.4 CanonicalHamiltonianFormulation 142
5.5 EliminationofMultipliers 145
5.6 Exercises 147
6 First-OrderVariationalPrinciples 151
6.1 VirtualVelocities 151
6.2 Jourdain’sPrincipleofVirtualPower 151
6.3 Kane’sFormulation 179
6.4 Exercises 185
7 Second-OrderVariationalPrinciples 188
7.1 VirtualAccelerations 188
7.2 Gauss’sPrinciple 188
7.3 Gauss’sPrincipleofLeastConstraint 201
7.4 Gibbs-AppellFormulation 206
7.5 Exercises 211
8 DynamicsinTaskSpace 214
8.1 TaskSpaceFramework 214
8.2 ConstrainedDynamicsinTaskSpace 227
8.3 Exercises 233
9 ApplicationstoBiomechanicalSystems 235
9.1 MusculoskeletalandNeuromuscularDynamics 235
9.2 ConstrainedDynamicsofBiomechanicalSystems 245
10 SoftwareforAnalyticalDynamics 263
10.1 GeneralPurposeMathematicalSoftware 263
10.2 DedicatedMultibodyDynamicsSoftware 268
Appendix InclusionofFlexibleBodies 269
A.1 ContinuumKinematics 269
A.2 ContinuumDynamics 270
A.3 SubsystemAssembly 273
References 275
Index 279
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Illustrations
1.1 Plateno.12ofBizzariediVarieFigure page2
1.2 Historicalprogressionofkeyprinciplesofanalyticaldynamics 4
1.3 Somedevicescomposedofbranchingkinematicchains 6
1.4 Somedevicesthatoperateunderholonomicconstraints 7
1.5 Somedevicesthatoperateundernonholonomicconstraints 8
2.1 TriangleABCdemonstratingthelawofcosines 11
2.2 Vectorcoordinateswithrespecttoabasis,B 14
2.3 Leastnormsolutionandspaceofallsolutions 19
2.4 Relationshipbetweenextrinsic,geodesic,andnormalcurvature 27
2.5 Ageodesicshowingzerogeodesiccurvature 28
2.6 MinimizationofJpxq“xTBxsubjecttotheconstraint,Ax“y 31
2.7 Twoparametricspacecurves ` ˘ 32
2.8 Implicitsurface f “4`x2``y2´ z´ 1cosp3xqcosp3yq 2 “0 ˘ 33
3
2.9 Parametricsurfacerpu,vq“ u,v,´2pu2`v2q`cosp2uqcosp2vq 34
5
2.10 Implicitsurface f “z´xy“0 34
3.1 RotationofframeBrelativetoframeA 37
3.2 Axis-anglerepresentationdescribinganarbitraryrotation 38
3.3 Euleranglesequence(xyz) 40
3.4 Differentialspin,(cid:2)θ,aboutafixedinstantaneousaxis 45
3.5 Instantaneousspinofabodyaboutanaxis 49
3.6 Firsttwoquaternioncomponentsderivedfromgyroscopedata 50
3.7 Lasttwoquaternioncomponentsderivedfromgyroscopedata 51
3.8 Eulerangle(β)timehistoryderivedfromgyroscopedata 52
3.9 Eulerangle(αandγ)timehistoryderivedfromgyroscopedata 53
3.10 Ahomogenoustransform 55
3.11 Ascrewdescription 56
3.12 Transformationsequenceofascrewdisplacement 57
3.13 Bodywithaccelerationcomponentsknownatthreedifferentlocations 61
3.14 Centerofmasspositionandorientationtimehistory 63
3.15 Centerofmassaccelerationxcomponent 63
3.16 Centerofmassaccelerationyandzcomponents 64
3.17 Centerofmassvelocityandpositionxcomponents 65
3.18 Centerofmassvelocityandpositionycomponent 66
3.19 Centerofmassvelocityandpositionzcomponent 67
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viii Illustrations
3.20 Reentrybodytrajectory 68
3.21 Coningangleofthereentrybody 68
3.22 Denavit-Hartenbergparameters 69
3.23 Branchingandclosedchainsystems 77
3.24 RotationofframeBrelativetoframeA 78
3.25 FramerepresentationsofaRRRjointmechanism 80
3.26 FramerepresentationsofaPRRjointmechanism 81
3.27 A2degree-of-freedomserialchainrobot(kinematics) 82
4.1 Free-bodydiagramshowingexternalforcesandmoments 85
4.2 Angularmomentumofabodyaboutanarbitraryoriginpoint 87
4.3 AconewithabaseradiusofRandheightofhinthezdirection 91
4.4 A3degree-of-freedomserialchainrobot 96
4.5 Animationframesandplotsfromthesimulationofaserialchainrobot 98
4.6 Acylindricaltubeandacuboid 99
4.7 A2degree-of-freedomserialchainrobot(dynamics) 100
5.1 Avirtualdisplacementofarigidbody 103
5.2 A4degree-of-freedomserialchainrobot 112
5.3 Animationframesandplotsfromthesimulationofaserialchainrobot 113
5.4 Constrainedstructuresinvolvingclosedloopsandalgebraic
dependencies 115
5.5 Configurationspaceconstrained-motionmanifold,Qp 116
5.6 Stewartplatformactuatedbysixprismaticstruts 119
5.7 Constraintforcesassociatedwithloopclosures 120
5.8 Parallelmechanismconsistingofserialchainswithloopclosures 122
5.9 Animationframesandplotsfromthesimulationofaparallel
mechanism 126
5.10 PlotsofLagrangemultipliersforaparallelmechanism 127
5.11 Agyroscopesupportedbyatwo-axisgimballedframe 135
5.12 Animationframesandplotsfromthesimulationofagimballed
gyroscope 139
5.13 Kineticandpotentialenergyandconservationoftotalenergy 140
5.14 A2degree-of-freedomserialchainrobot(d’Alembert) 147
5.15 Atwo-linkplanarslider-crankmechanism 148
5.16 Aplanarfour-barlinkage 149
5.17 Athree-linkplanarslider-crankmechanism 149
6.1 Avirtualvelocityofarigidbody 153
6.2 Arollingdiskwithnonholonomicconstraints 164
6.3 Animationframesandplotsfromthesimulationofanonholonomic
rollingdisk 167
6.4 Constraintforcesexertedonthediskatthecontactpoint 168
6.5 Arollingballwithnonholonomicconstraints 168
6.6 Animationframesandplotsfromthesimulationofarollingball 170
6.7 Plotsoftheorientationofarollingballandmomentwheelangles 172
6.8 Twowheelsconnectedbyanaxlewithnonholonomicconstraints 173
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Illustrations ix
6.9 Animationframesandplotsfromthesimulationoftheaxleandrolling
wheels 177
6.10 Plotsofthewheelanglesfortherollingwheelassembly 178
6.11 Arollingdiskwithnonholonomicconstraints(Kane’smethod) 182
6.12 Animationframesandplotsfromthesimulationofarollingdisk
(Kane’smethod) 184
6.13 Asimplifiedversionoftherollingdisk 185
6.14 Atwo-wheeledapparatus 186
7.1 Avirtualaccelerationofarigidbody 190
7.2 TheGaussfunction,G,minimizedsubjecttotheconstraints 202
7.3 Geodesicforce-freepathsonaconstrained-motionmanifold 204
7.4 Solvingforgeodesicforce-freepathsonaconstrained-motion
manifold 206
7.5 Arollingdiskwithnonholonomicconstraints(Gibbs-Appellmethod) 210
7.6 Aplanarfour-barlinkage(Gauss) ` ˘ 212
7.7 Implicitsurfaceφ “4`x2`y2´ z´ 1cosp3xqcosp3yq 2 “0 212
3
7.8 Asimplifiedversionoftherollingdisk(Gibbs-Appellmethod) 213
8.1 Taskdescriptionsforserialandbranchingchains 215
8.2 A4degree-of-freedomserialchainrobot(taskspacedynamics) 217
8.3 Animationframesandplotsfromthesimulationofaserialchainrobot 218
8.4 Plotsoftherobottaskspacegravityvector 219
8.5 A3degree-of-freedomserialchainrobot(taskspacedynamics) 221
8.6 Kineticenergyellipsoidsforasequenceofconfigurations 222
8.7 Beltedellipsoidsforasequenceofconfigurations 223
8.8 Taskdescriptionforamultibodysystemwithloopconstraints 227
8.9 Parallelmechanism(taskspacedynamics) 231
8.10 Animationframesandplotsfromthesimulationofaparallel
mechanism 232
8.11 A2degree-of-freedomserialchainrobot(taskspacedynamics) 233
8.12 Atwo-linkplanarslider-crankmechanism(taskspacedynamics) 234
9.1 Activestatemusculotendonmodel 237
9.2 Neuromuscularandmusculoskeletalsystem(feed-forwardpath) 238
9.3 Simplifiedmodelofthehumanarmconsistingofthreegeneralized
coordinates 240
9.4 Simplifiedmodelofthehumanarmactuatedby24muscles 242
9.5 Muscleforce-length-ratesurfaceatfullactivation 243
9.6 Animationframesandplotsfromthearmsimulation 244
9.7 Plotsofneuralexcitationsandmuscleactivations 245
9.8 Variousconstituentsoftheshouldercomplex 247
9.9 Parameterizationofashouldermodel 248
9.10 Musclepathsspanningtheshouldercomplex 252
9.11 Musclemomentarmsforthedeltoidmuscles 254
9.12 Muscleforcesandmomentcapacitiesforthedeltoidmuscles 255
9.13 Parallelandserialpartsofahumanoidshouldercomplex 256
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