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时间:2019-03-02
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1、MechanismandMachineTheoryMechanismandMachineTheory41(2006)41–52www.elsevier.com/locate/mechmtAnhistoricalreviewofthetheoreticaldevelopmentofrigidbodydisplacementsfromRodriguesparameterstothefinitetwistJianS.Dai*DepartmentofMechanicalEngineering,SchoolofPhysicalScien
2、cesandEngineering,King’sCollegeLondon,UniversityofLondon,Strand,LondonWC2R2LS,UKReceived5November2004;receivedinrevisedform30March2005;accepted28April2005Availableonline1July2005AbstractThedevelopmentofthefinitetwistorthefinitescrewdisplacementhasattractedmuchattenti
3、oninthefieldoftheoreticalkinematicsandtheproposedq-pitchwiththetangentofhalftherotationanglehasdem-onstratedanelegantuseinthestudyofrigidbodydisplacements.ThisdevelopmentcanbedatedbacktoRodriguesÕformulaederivedin1840withRodriguesparametersresultingfromthetangentofh
4、alftherota-tionanglebeingintegratedwiththecomponentsoftherotationaxis.ThispapertracestheworkbacktothetimewhenRodriguesparameterswerediscoveredandfollowsthetheoreticaldevelopmentofrigidbodydisplacementsfromtheearly19thcenturytothelate20thcentury.Thepaperreviewsthewo
5、rkfromChaslesmotiontoCayleyÕsformulaandthentoHamiltonÕsquaternionsandRodriguesparameterizationandrelatestheworktoCliffordbiquaternionsandtoStudyÕsdualangleproposedinthelate19thcentury.Thereviewoftheworkfromthesemathematiciansconcentratesonthedescriptionandthereprese
6、ntationofthedisplacementandtransformationofarigidbody,andonthemathematicalformulationanditsprogress.Thepaperfurtherrelatesthishistoricdevelopmenttothecontemporarydevelopmentofthefinitescrewdisplacementandthefinitetwistrepresentationinthelate20thcentury.Ó2005ElsevierL
7、td.Allrightsreserved.*Tel.:+44(0)2078482321;fax:+44(0)2078482932.E-mailaddress:jian.dai@kcl.ac.ukURL:http://www.eee.kcl.ac.uk/mecheng/jsd.0094-114X/$-seefrontmatterÓ2005ElsevierLtd.Allrightsreserved.doi:10.1016/j.mechmachtheory.2005.04.00442J.S.Dai/MechanismandMach
8、ineTheory41(2006)41–52Keywords:Theoreticalkinematics;Rotations;Transformationgroup;Screw;Finitetwist;Finitescrewdisplacement;Rigidbodydisplacemen
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