小型物料運(yùn)送手臂設(shè)計(jì)【搬運(yùn)機(jī)械手】【氣動(dòng)方式驅(qū)動(dòng)】【自由度可變】【說(shuō)明書(shū)+CAD+SOLIDWORKS+仿真】,搬運(yùn)機(jī)械手,氣動(dòng)方式驅(qū)動(dòng),自由度可變,說(shuō)明書(shū)+CAD+SOLIDWORKS+仿真,小型物料運(yùn)送手臂設(shè)計(jì)【搬運(yùn)機(jī)械手】【氣動(dòng)方式驅(qū)動(dòng)】【自由度可變】【說(shuō)明書(shū)+CAD+SOLIDWORKS+仿真】,小型,物料 Akeypointdimensionaldesignmethodofa6-DOFparallel manipulatorforagivenworkspace RuiCao 1 ,FengGao ,1 ,YongZhang 1 ,DaleiPan 1 StateKeyLabofMechanicalSystemandVibration,SchoolofMechanicalEngineering,ShanghaiJiaoTongUniversity,Shanghai,PRChina article info abstract Articlehistory: Received3April2014 Receivedinrevisedform7November2014 Accepted8November2014 Availableonline25November2014 This paper presents a new method of dimensional design for a 6-PSS parallel mechanism according toagivenworkspace.Asymmetricaldescriptionhasbeen foundtodescribe the6-D workspace concisely for the dimensional design. Many key point characteristics have been found and veri ed by the kinematic analysis and the method of Lagrange multipliers. Furthermore,thedirectrelationsbetweenthegivenworkspaceandthemanipulatorsgeometrical parametershavebeenderived.Theproposeddesignmethodwhichisbasedonthesekeypoint characteristicshasveryhighef ciencyand accuracy.Additionally,theavoiding ofthecomplex analysisofthemanipulatorsworkspaceandthedimensionlessderivationmake thepossibility ofwideuseofthismethod. 2014ElsevierLtd.Allrightsreserved. Keywords: Parallelmanipulator Dimensionaldesign Workspace 6-PSS Keypoint 1.Introduction Theinterestforparallelmanipulatorsarisesfromthefactthattheyhavebetterload-carryingcapacity,betterstiffness,andbetter precision than serial manipulators 14. Thus the research on designing parallel manipulators has become a hot topic in the international roboticresearcharea 59. Thedesign ofparallelmanipulators is a challengingproblemin the machinery product designprocess.Thetypesynthesisisfordesigningthecon gurationformanipulators1012.Andthenthegeometricalparameters ofmanipulatorsshouldbedeterminedbythedimensionaldesign.Becausethetypesofparallelmechanismsarealmostunlimited,the dimensionaldesignmustbebasedonacertaintypeofmechanisms.Theparameterdesignmethodspresentedinreference13,14are basedon6-DOFGough-typemanipulatorsand3-DOFparallelmanipulators,respectively. Generally, one of the most important design objectives is to let the manipulator work in a given workspace. Therefore, the dimensionaldesignofparallelmanipulatorsforagivenworkspaceisanimportantproblem,whichhasnotgainedtoomuchinterest. Sofar,therearemainlytwowaystodesignthegeometricalparametersofparallelmanipulatorsaccordingtoagivenworkspace.The rstoneusesmanypointstodescribethegivenworkspaceandthencheckwhetherthemanipulatorwithcertainparameters tsthe design requirements at each point 1517. The other one establishes a function between the parameters and the workspace boundaries of the manipulator, then make sure that the given workspace is within the manipulators workspace boundaries 1822.Basedonseveralkeypointsthatwehavefoundinthisstudy,thispaperattemptstoexploreanewwayofdimensionaldesign foranew6-DOFparallelmanipulatoraccordingtoagivenworkspace.Thisdesignmethodisfastanditsresultisaccurate. Inour previouswork,anewtype of6-DOFparallelmechanismwithanorthogonal 3-3-PSScon gurationhasbeenproposed. Compared with the traditional 6-SPS parallel manipulators, this 3-3-PSS parallel manipulator allows higher isotropy of the manipulatorsperformance,largerrotationrangeofthemovingplatformandlessbodyinertia. MechanismandMachineTheory85(2015)113 Correspondingauthor. E-mailaddresses:(R.Cao),(F.Gao),(Y.Zhang),(D.Pan). 1 P.O.BoxME290,MechanicalBuilding,ShanghaiJiaoTongUniversity,No.800DongchuanRoad,Shanghai200240,PRChina. http:/dx.doi.org/10.1016/j.mechmachtheory.2014.11.004 0094-114X/2014ElsevierLtd.Allrightsreserved. ContentslistsavailableatScienceDirect MechanismandMachineTheory journalhomepage:Tobeginthedesign,therequiredworkspaceshouldbeclearlydescribed.Becausethe6-dimensionalworkspacecannotberepresent- edgraphicallyinahuman-readablewayandtherearenogeneralwaytoanalyticallydeterminetheboundariesofthe6-Dworkspacefor 6-DOFparallelmanipulators,mostliteratures2327dividethe6-Dworkspaceintopositionworkspaceandorientationworkspace.The position workspace refers to a space that the manipulators moving platformcan reach with a certain orientation. And it can be easily depicted.Theorientationworkspaceisthecollectionofalltheorientationsthatthemovingplatformcanachieveatacertainpoint.How- ever,duetothecomplexityoftherotatingangles,theorientationworkspaceisdif culttobedeterminedandrepresented.Considering the symmetry of ourparallel manipulator, a concise way of describingthe 6-D workspace is found for the dimensional design. Thepaperisorganizedasfollows.Section2introducesthemodelingofthedesignproblemandthekinematicsanalysis.Section3 shows how the key point characteristics are found. The design method and its application are discussed in Section 4.Finally, concludingremarksarepresentedinSection5. 2.Modelingofthedesignproblemandkinematicanalysis Thearchitectureofthenew3-3-PSSparallelmanipulatorisshowninFig.1,whichiscomposedofamovingplatform,a xedbase, andsixsupportinglimbswithidenticalgeometricalstructure.Thelimbsarenumberedfrom1to6.Eachlimbconnectsthe xedbase tothemovingplatformbyaprismaticjoint,asphericaljointB i andasphericaljointA i inseries.Alinearactuatoractuatestheprismatic jointofeachlimbalonga xedrail.BetweenthejointB i andjoint A i isa rigidlinkoflength L i (i=1,6). Thethreelinearactuatorsofthelimbs1,2,and3arearrangedwiththeiraxeslocatedinahorizontalplaneP B ,andtheanglesbe- tweeneachoftheiraxesare120whiletheseaxesdonotintersectatonepoint.Thedistancesbetweentheseaxesandthesymmetry axisofthemanipulatorarethesame,andhereweusetheparameteratorepresentthisdistance.Theotherthreelinearactuatorsof thelimbs4,5,and6arearrangedwiththeiraxesvertically.Thecentersofthejoints A 1 A 6 ofthemovingplatformaredistributed symmetricallyonacircleofradius a.Thecenterofthismanipulatorisattheintersectionoftheplane P B andthesymmetryaxisof themanipulator,onwhichattacheda xedCartesianreferencecoordinateframeOx,y,z.The xedframes y-axis and z-axis are in theplane P B ,andits x-axiscoincideswiththesymmetryaxisofthemanipulator.AmovingframeO x,y,zisattachedonthe movingplatformatpointOwhichisthecenterofthecirclethatpointsA 1 A 6 locatedon.Consideringthefactthatthemanipulator isaxisymmetric,letpoint OcoincideswithpointOwhenthemovingplatformisattheinitialposition.Thustheworkspaceofthe manipulatorisalsoaxisymmetricwithrespecttothe xedframeO. Beforedesigningthegeometricalparametersofthemanipulator,therequiredworkspaceshouldbeclearlydescribed.Ascanbe seenfromthepreviousdiscussion,conciselydescribingthe required6-Dworkspaceisachallengingproblem.Inthisresearch,for the orientationdescriptionofthe moving platform, onlythe pointing vector(showed inFig.2) rather thanthe rotation aboutits symmetryaxisisconcerned.Infactthishasthesamesituationformanymachinetools.Basedonthis,weuseaspecialsetofEuler anglestorepresenttheorientationofthemovingplatform.Themovingplatform rstrotatesaboutthe xedx-axisbyanangle-, thenaboutthe xedz-axisbyanangle,and nallyaboutthe xedx-axisbytheangle(Fig.2).Andwecansimplywritetherotation matrixforthiscaseas: R Rot x; Rot z; Rot x; c cs ss cs s 2 c 2 csscc ss csccs c 2 s 2 c 2 4 3 5 ; 1 Fig.1.Thecon gurationoftheproposed 3-3-PSSparallelmanipulator. 2 R.Caoetal./MechanismandMachineTheory85(2015)113wherecstandsforcosine,sstandsforsine,and0,respectively.Fortheconvenienceofdescription,Eq.(1)canbe abbreviatedas R r 11 r 12 r 13 r 21 r 22 r 23 r 31 r 32 r 33 2 4 3 5 : 2 Andit can be observed that r 32 r 23 sin 2 1cos 2 : 3 ThisspecialsetofEuleranglesgivesanintuitiverepresentationofthemovingplatformsorientation.Thepointingvectorisdecid- edbyand.Duetothesymmetryofthemanipulator,itiseasyto ndoutthattherangeofisunlimitedwhileisnot.Thus,allthe possiblepointingvectorsthatthemovingplatformcanachieveatacertainpointconstituteacone.Andtheapertureoftheconeisonly relatedtothemaximumrangeofwhichisrepresentedby m .Wecall m asthepointingdexterityindexofthemovingplatform. To take advantage of the symmetry of the manipulator, we restrict the required workspace as a symmetric space. Hence, we describethegivenworkspaceasacylinderwithradiusofR c ,andheightof2H c .Additionally,themanipulatorshouldhavethepointing dexterityof m atanypointwithinthiscylinder.Thishuman-readableworkspacedescription tsforthemanipulatorssymmetryand makesthedesignobjectiveclearly.Knowingthatthisworkspacedescriptionisactually5-DOF,torepresenta6-DOFworkspace,an additionaldexterityindexoftherotationaboutthemovingplatformssymmetryaxisisneeded.Inthissituation,themovingplatform should rstperformanadditionalrotationaboutthe xedx-axisbyanangle,andtherotationmatrixcanbewrittenasRot(x,) Rot(z,)Rot(x,-)Rot(x,).However,5-DOFisenoughforourcurrentstudyandmostmulti-DOFmachinetools. Aftertheanalysisoftherequiredworkspace,whatparametersofthemanipulatorneedtobedeterminedshouldbeclari ed.The followingpartwill ndthisoutbyanalyzingthekinematicsofthemanipulator.Asthesixlimbsofthemanipulatorhaveidentical geometricalstructure, wecanchoose onetypicallimbfortheanalysisanditsvectorsaredescribed inFig. 3. Thelinearactuators axisisrepresentedby e i whichisaunitvector.Thedirectionoftherigidlinkisrepresentedby l i whose magnitude is L i .Thevector between O and the center of the joint A i is represented by a i with respect to the moving frame O , and a i with respect to the xedframe O.Itcanbefoundfromthepreviouspartthatthemagnitudeof a i /a i is a.Whenthemanipulatorattheinitialposition thatmentionedabove,e i (i= 1,2,3)isperpendiculartoa i ,itshouldbenoted.AndtheinitialpositionofB i inthissituationisrepresent- edbypointC i whosepositionvectoris c i .WiththespecialsetofEulerangles,thetransformationfromthemovingframetothe xed framecanbedescribedbythepositionvectorofthemovingplatformp=P x P y P z T ,andtherotationmatrixR.Thusthegeneralized coordinatesofthemovingplatformcanbedescribedas(P x ,P y ,P z ,0). Letq i representthestrokeofthelinearactuator.ThenwecansimplygetthefollowingrelationfromFig. 3: l i pRa 0 i q i e i c i : 4 In some cases, the joints B i and A i whose stiffness are the lowest of the manipulator need a strong structure to increase their stiffness. However, the strong structure always limits the rotation ranges of these joints. Therefore, the swing amplitude of the Fig.2.ThepointingdexterityandthespecialsetofEulerangles. 3 R.Caoetal./MechanismandMachineTheory85(2015)113rigidlinkshouldbestudied.Wede netheanglebetween l i and e i asthejointangle Bi ofjointB i .AsjointA i is xedonthemoving platform,thede nitionshouldwithrespecttothemovingframeOx,y,z.Thusthejointangle Ai ofjointA i isde nedastheangle between l i and Re i . Bi and Ai are depicted in Fig. 3. The following equations about Bi and Ai can be achieved by their de ni- tion: l i e i L i cos Bi 5 l i Re i L i cos Ai : 6 Accordingtothesede nitions,therotationoftherigidlinkaboutitsownaxisl i isnotinvolved.So Bi and Ai representtheswing amplitudeoftherigidlinkwithrespecttotheconnectingjoint.Themaximumvaluesof Bi and Ai areveryimportantforthedesignof thesphericaljointsandmeaningfulforavoidingtheinterferencebetweentherigidlinks. Thesixlimbscanbedividedintotwogroupsaccordingtothecon gurationofthemanipulator.Thelimbs1,2,and3arecontained ingroup1,andthelimbs4,5,and6ingroup2.Thesetwogroupshavedifferentkinematiccharacteristics,thusneedtobestudied separately. For the sake of symmetry, the rigid links in one group should have the same length. In group 1 for i=1,2and3,a xed Cartesian reference coordinate frame O ai x, y, z is attached at the point O. For simplicity andwithoutlosing the generality, we let its y-axis point in the negative direction of the vector e i and let its x-axis coincide with the x-axis of the frame Ox, y, z. Withrespecttotheframe O ai ,itcanbeknownfromthearchitectureofthemanipulatorthat e i 0 10 T , a 0 i 00a T and c i 0 L i a T . Assume that l i l x l y l z T . Substituting all the known variables into Eq. (4) yields the following equations: l x ar 13 p x 7 l y ar 23 p y L i q i 8 l z ar 33 ap z : 9 Furthermore,thefollowingrelationcanbeachievedwiththefactthatL i isthemagnitudeofvector l i : l y L 2 i l 2 x l 2 z q : 10 AccordingtoEq. (10),l y hastwopossiblesolutions.WhenacoordinateofthemovingplatformmakesL i 2 l x 2 l z 2 b0,l y hasno solution, whichmeansthat thiscoordinateisoutofthemanipulatorsreachableworkspace.The situationL i 2 l x 2 l z 2 =0means that the moving platform reaches the boundary of the reachable workspace. This situation is singular and should be avoided in Fig.3.Onetypicallimbofthemanipulator. 4 R.Caoetal./MechanismandMachineTheory85(2015)113