Dual Quaternions as a Tool for Rigid Body Motion Analysis.pdf

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1、MULTIBODYDYNAMICS2009,ECCOMASThematicConferenceK.Arczewski,J.Fr˛aczek,M.Wojtyra(eds.)Warsaw,Poland,29June–2July2009DUALQUATERNIONSASATOOLFORRIGIDBODYMOTIONANALYSIS:ATUTORIALWITHANAPPLICATIONTOBIOMECHANICSEttorePennestrì,PierPaoloValentiniDipartimentod

2、iIngegneriaMeccanicaUniversitàRomaTorvergataviadelPolitecnico,1,00133Roma,Italye-mail:pennestri@mec.uniroma2.ite-mail:valentini@ing.uniroma2.itKeywords:Biomechanics,Humanmotionanalysis,Cliffordalgebra,DualquaternionsAbstract.Dualquaternionsanddualquat

3、ernioninterpolationarepowerfulmathematicaltoolsforthespatialanalysisofrigidbodymotions.Inthispaper,afterareviewofsomebasicresultsandformulas,itwillbepresentedanattempttousethesetoolsforthethekinematicmodelingofhumanjoints.Inparticular,thekinematicpara

4、metersextractedfromexperimen-tallyacquireddataarecomparedwiththosetheoreticallycomputedfromdualquaternionsrigidbodymotioninterpolation.1EttorePennestrì,PierPaoloValentini1INTRODUCTIONRigidbodyspatialrotationsandscrewmotionscanbedescribedbymeansofdiffe

5、rentmath-ematicalentitiessuchasmatrices,quaternions,dualvectorsanddualquaternions[1,2].Inthispapertheuseofdualquaternionsforthedescriptionofscrewdisplacementswillbediscussedwithanapplicationtohumanmotionanalysis.Themathematicaldefinitionofrelativemotio

6、nbetweenhumanbodysegmentsisacomplextask.Thisisduetothepeculiarshapeofthekinematicelementsformingcartilagineousandsynovialjoints.Forthisreason,inthedevelopmentofmathematicalmodels,acommonap-proachisthereplacementofsuchjointswiththosewhosemodelingissimp

7、lified.Forinstance,thekneejointisusuallysubstitutedbyanhingejoint,asshowninFigure1.1Figure1:Kinematicmodelingofaknee-jointThisinvestigationhasthepurposetoexploretheuseofrigidbodymotioninterpolationmethodsforthemathematicalmodelingofelbowjoints.Inpartic

8、ular,theapproachhereinpresentedcanbeappliedtolocatetherotationaxisoftherelativemotionbetweenhumansegments.Themethodisvalidforathreedimensionalmotionanddoesnotrequirethehypothesisofplanarmotion,asthoseproposedin[3,4].Thispaperismainlydividedint