Quality index and kinematic analysis of spatial redundant in-parallel manipulators

167 Pages·2000·6.2 MB·English

by  Zhang, Yu,

QUALITYINDEXANDKINEMATICANALYSISOF
SPATL\LREDUNDANTIN-PARALLELMANIPULATORS
i-'-
:' *: ''if:' ^K
By
YUZHANG
ADISSERTATIONPRESENTEDTOTHEGRADUATESCHOOL
OFTHEUNIVERSITYOFFLORIDAINPARTIALFULFILLMENT
OFTHEREQUIREMENTSFORTHEDEGREEOF
DOCTOROFPHILOSOPHY
UNIVERSITYOFFLORIDA
2000
Copyright2000
by
YuZhang
Tomywife,Ying,andourparents.
ACKNOWLEDGMENTS
I want to express my deep and sincere gratitude to Dr. Joseph Duffy, my
supervisorduringmyPh.D.study,forprovidingmewiththeopportunitytocompletemy
study under his exceptional guidance. Without his untiring patience, constant
encouragement, guidance and knowledge this workwould not havebeen possible. I
wouldalsoliketothankmysupervisorycommitteemembers.Dr. CarlD. Crane,Dr.
GloriaJ. Wiens, Dr. Ali A. Seirig, and Dr. Ralph Selfridge. I am grateful fortheir
willingnessto serve on mycommittee, providingme help wheneverneeded and for
reviewing this dissertation. I especially thank Professor Chonggao Liang ofBeijing
UniversityofPostsandTelecommunicationsforeducatingmeonthevariousaspectsof
mechanismanalysisanddesign. Also, Iwouldliketothankallmycolleaguesinthe
CenterforIntelligentMachinesandRoboticsfortheirhelpandsupport.
Finally,Iwouldliketothankmylovelywife,YingZhu.Herlove,supportand
encouragementhashadmademyliferichandcomplete.Iamgratefultomyparentsand
parents-in-lawfortheirconstantsupportandencouragementthroughoutmyeducational
endeavors.
IV
TABLEOFCONTENTS
ACKNOWLEDGMENTS iv
LISTOFTABLES vii
LISTOFFIGURES viii
ABSTRACT xi
LINTRODUCTION 1
1.1RedundantParallelManipulators 1
1.2QualityIndex 6
1.3OutlineofDissertation 9
2.SPATL\LGEOMETRYANDSTATICS 12
2.1PliickerLineCoordinates 12
2.2StaticsofaRigidBody 15
2.3TheStaticsofaParallelManipulator 20
3.THEOPTIMUMQUALITYINDEXFORASPATIALREDUNDANT
4-4IN-PARALLELMANIPULATOR 24
3.1Determinationof-ydetJ^J^ 25
3.2Implementation 30
4.THEKINEMATICANALYSISOFTHESPATIALREDUNDANT
4-4IN-PARALLELMANIPULATOR 43
4.1InverseKinematicAnalysis 44
4.2ForwardKinematicAnalysis 47
4.2.1Introduction 47
4.2.2CoordinateTransformations 48
4.2.3ConstraintEquations 51
4.2.4TheSolution 52
4.2.5NumericalVerification 55
5.THEOPTIMUMQUALITYINDEXFORASPATIALREDUNDANT
4-8IN-PARALLELMANIPULATOR 58
5.1DeterminationofydetJ^J^ 59
5.2Implementation 64
6.THEFORWARDKINEMATICANALYSISOFTHESPATIALREDUNDANT
4-8IN-PARALLELMANIPULATOR 79
6.1ForwardKinematicAnalysis 79
6.2NumericalVerification 82
7.THEOPTIMUMQUALITYINDEXFORASPATIALREDUNDANT
8-8IN-PARALLELMANIPULATOR 85
7.1Determinationof^detJ^J^ 85
7.2Implementation 94
8.THEFORWARDKINEMATICANALYSISOFTHESPATL\LREDUNDANT
8-8IN-PARALLELMANIPULATOR 110
8.1CoordinateSystems 110
8.2ConstraintEquations 113
8.3EquationSolution 114
8.4NumericalVerification 118
9.CONCLUSIONS 121
APPENDIXA:CONSTANTSFORTHEFORWARDKINEMATICANALYSISOF
THEREDUNDANT4-4IN-PARALLELMANIPULATOR 123
APPENDIXB:CONSTANTSFORTHEFORWARDKINEMATICANALYSISOF
THEREDUNDANT8-8IN-PARALLELMANIPULATOR 130
LISTOFREFERENCES 148
BIOGRAPHICALSKETCH 152
VI
LISTOFTABLES
Table Page
Table4.1:Numericalresultsoftheredundant4-4in-parallelmanipulator 56
Table4.2:Anumericalexampleforthespecialcaseoftheredundant4-4in-parallel
manipulator 57
Table6.1:Numericalresultsoftheredundant4-8in-parallelmanipulator 83
Table6.2:Anumericalexampleforthespecialcaseoftheredundant4-8in-parallel
manipulator 84
Table8.1:Numericalresultsoftheredundant8-8in-parallelmanipulator 119
Table8.2:Anumericalexampleforthespecialcaseoftheredundant8-8in-parallel
manipulator 119
vu
1
LISTOFFIGURES
Figure Page
Figure1.1:Aplanarparallelx-ymanipulatorwithoneredundantactuator 2
Figure1.2:A2-DoFplanarparallelmanipulator 3
Figure1.3:Aredundant2-DoFplanarparallelmanipulator 3
Figure1.4:Planarviewofspatialnonredundant4-4in-parallelmanipulators 4
Figure1.5:Self-deployablespacestructure 1
Figure2.1:Determinationofaline 13
Figure2.2:Pliickerlinecoordinates 15
Figure2.3:Representationofaforceonarigidbody 16
Figure2.4:Dynameandwrench 19
Figure2.5:A6-6in-parallelmanipulator 21
Figure3.1:Aredundant4-4in-parallelmanipulator 24
Figure3.2:Planviewoftheredundant4-4in-parallelmanipulator 24
Figure3.3:Planviewoftheoptimalconfigurationoftheredundant4-4in-parallel
manipulatorwiththemaximumqualityindex 30
Figure3.4:Qualityindexforplatformverticalmovement 31
Figure3.5:Qualityindexforplatformhorizontaltranslation 34
Figure3.6:Platformrotationsaboutthe^''-axis 35
Figure3.7:Qualityindexforplatformrotationsaboutthea:'-and>''-axes 37
Figure3.8:Platformrotationsaboutthez-axis 38
Vlll
Figure3.9:Qualityindexforplatformrotationaboutthez-axis 40
Figure3.10:Planviewofthesingularitypositionoftheredundant4-4in-parallel
manipulatorwhen6z=90° 41
Figure4.1:Coordinatesystemsofaredundant4-4in-parallelmanipulator 45
Figure4.2:Coordinatetransformations 49
Figure5.1:Aredundant4-8in-parallelmanipulator 58
Figure5.2:Planviewoftheredundant4-8in-parallelmanipulator 58
Figure5.3:Planviewoftheoptimalconfigurationoftheredundant4-8in-parallel
manipulatorwiththemaximumqualityindex 63
Figure5.4:Compatibilitybetweentheredundant4-4andthe4-8parallelmanipulators.64
Figure5.5:Qualityindexforplatformverticalmovement 65
Figure5.6:Qualityindexforplatformhorizontaltranslationwithdifferentvaluesofj5.70
Figure5.7:Platformrotationaboutthey'-axis 71
Figure5.8:Quahtyindexforplatformrotationsaboutthejc'-andj'-axes 73
Figure5.9:Platformrotationaboutthez-axis 74
Figure5.10:Qualityindexforplatformrotationaboutthez-axis 76
Figure5.11:Planviewofthesingularitypositionoftheredundant4-8in-parallel
manipulatorwhen^^=90° 77
Figure6.1:Coordinatesystemsofaredundant4-8in-parallelmanipulator 80
Figure6.2:Legrelations 81
Figure7.1:Aredundant8-8in-parallelmanipulator 86
Figure7.2:Planviewoftheredundant8-8in-parallelmanipulator 86
Figure7.3:Plotof/(a,/3)=2aj3-2a-2/3+\= 90
Figure7.4:Plotof/ivs.aandyffwitha=1 92
Figure7.5:PlotofV^etJ^J^ vs.av/kha=1 93
Figure7.6:Anexampleofredundant8-8manipulatorinoptimalconfiguration... 93
IX
Figure7.7:Qualityindexforplatformverticalmovement 96
Figure7.8:Reductionofthesizeoftheredundant8-8in-parallelmanipulator 96
Figure7.9:QualityindexforplatformhorizontaltranslationwithdifferentvaluesofalOO
Figure7.10:Platformrotationsaboutthe>''-axis 102
Figure7.11:Qualityindexforplatformrotationsaboutthex'-and>''-axes 105
Figure7.12:Platformrotationsaboutthez-axis 106
Figure7.13:Qualityindexforplatformrotationaboutthez-axis 108
Figure7.14:Planviewofthesingularitypositionofredundant8-8in-parallel
manipulatorwhen6^=90° 109
Figure8.1:Coordinatesystemsofaredundant8-8in-parallelmanipulator Ill