工业机器人手臂的静态平衡英文文献

ThestaticbalancingoftheindustrialrobotarmsPartI:DiscretebalancingIonSimionescu*,LiviuCiupituMechanicalEngineeringDepartment,POLITEHNICAUniversityofBucharest,SplaiulIndependentei313,RO-77206,Bucharest6,RomaniaReceived2October1998;accepted19May1999AbstractThepaperpresentssomenewconstructionalsolutionsforthebalancingoftheweightforcesoftheindustrialrobotarms,usingtheelasticforcesofthehelicalsprings.Forthebalancingoftheweightforcesoftheverticalandhorizontalarms,manyalternativesareshown.Finally,theresultsofsolvinganumericalexamplearepresented.72000ElsevierScienceLtd.Allrightsreserved.Keywords:Industrialrobot;Staticbalancing;Discretebalancing1.IntroductionThemechanismsofmanipulatorsandindustrialrobotsconstituteaspecialcategoryofmechanicalsystems,characterisedbybigmasselementsthatmoveinaverticalplane,withrelativelyslowspeeds.Forthisreasontheweightforceshaveahighshareinthecategoryofresistancethatthedrivingsystemmustovercome.Theproblemofbalancingtheweightforcesisextremelyimportantfortheplay-backprogrammablerobots,wherethehumanoperatormustdriveeasilythemechanicalsystemduringthetrainingperiod.Generally,thebalancingoftheweightforcesoftheindustrialrobotarmsresultsinthedecreaseofthedrivingpower.ThefrictionalforcesthatoccurinthebearingsarenottakenMechanismandMachineTheory35(2000)1287±12980094-114X/00/$-seefrontmatter72000ElsevierScienceLtd.Allrightsreserved.PII:S0094-114X(99)00067-1*Correspondingauthor.E-mailaddress:[e-mail](I.Simionescu).intoconsiderationbecausethefrictionalmomentsensesdependontherelativemovementsenses.Inthiswork,somepossibilitiesofbalancingoftheweightforcesbytheelasticforcesofthecylindricalhelicalspringswithstraightcharacteristicsareanalysed.Thisbalancingcanbemadediscretely,fora®nitenumberofwork®eldpositions,orincontinuousmodeforallpositionsthroughoutthework®eld.Consequently,thediscretesystemsrealisedonlyanapproximativelybalancingofthearm.Theuseofcounterweightsisnotconsideredsincetheyinvolvetheincreaseofmovingmasses,overallsize,inertiaandthestressesofthecomponents.2.Thebalancingoftheweightforceofarotatinglinkaroundahorizontal®xedaxisThereareseveralpossibilitiesofbalancingtheweightforcesofthemanipulatorandrobotarmsbymeansofthehelicalspringelasticforces.Thesimplesolutionsarenotalwaysapplicable.Sometimesanapproximatesolutionispreferred,leadingtoaconvenientalternativefromconstructionalpointofview.Thesimplestbalancingpossibilityoftheweightforceofalink1(thehorizontalrobotarm,forexample)whichrotatesaroundahorizontal®xedaxisisschematicallyshowninFig.1.Ahelicalspring2,joinedbetweenapointAofthelinkanda®xedBone,isused.Theequationthatexpressestheequilibriumoftheforcesmoments[1],whichacttothelink1,isÿm1OG1cosji‡m2AXA
g‡Fsaˆ0,iˆ1,...,6,…1†wheretheelasticforceofthehelicalspringis:FsˆF0‡k…ABÿl0†,andFig.1I.Simionescu,L.Ciupitu/MechanismandMachineTheory35(2000)1287±12981288aˆXBYAÿXAYBAB;XAYAˆRjix1Ay1A;Rjiˆcosjiÿsinjisinjicosji;ABˆ…XAÿXB†2‡…YAÿYB†2q;m2AˆBG2ABm2:ThegravitycentreG2ofspring2iscollinearwithpairscentresAandB.Thesti€nesscoecientofthespringisdenotedbyk,m1isthemassofthelink1,m2isthemassofthehelicalspring2,andgrepresentsthegravityaccelerationmagnitude.Thus,theunknownfactors:x1A,y1A,XB,YB,F0andkmaybecalculatedinsuchawaythattheequilibriumoftheforcesisobtainedforsixdistinctvaluesoftheangleji:Themovableco-ordinateaxissystemx1Oy1attachedtothearm1waschosensothatthegravitycentreG1isupontheOx1axis.Theco-ordinatesx1Aandy1Ade®nedthepositionofpointAofthearm1.Intheparticularcase,characterisedbyy1AˆXBˆl0ˆF0ˆ0,theproblemallowsanin®nitenumberofsolutions,whichverifytheequation:kˆ…m1OG1‡m2Ax1A†gx1AYB,foranyvalueofanglej:Sinceinthiscase,FsˆkAB(seeline1,Fig.2),somedicultiesariseintheconstructionofthissystemwhereitisnotpossibletouseahelicalextensionspring.Thecompressionspring,whichhastocorrespondtothecalculatedfeature,mustbepreventedagainstbuckling.Consequently,thefrictionforcesthatappearintheguidesmakethetrainingoperationmoredicult.Eveninthegeneralcase,wheny1A6ˆ0andXB6ˆ0,resultsareducedvalueoftheinitiallengthl0ofthespring,correspondingtotheforcesF0ˆ0:Themodi®cationofthestraightcharacteristicpositiontothenecessaryspringforbalancing(line2,Fig.2),i.e.toobtainanacceptableinitiallengthl0fromtheconstructionalpointofview,maybeachievedbyreplacingthe®xedpointBofspringarticulationbyamovableone.Inotherwords,thespringwillbearticulatedwithitsBendofamovablelink2,whosepositiondependsonthatofthearm1.Link2mayhavearotationalmotionarounda®xedaxis,aplane-paralleloratranslationalone,anditisdrivenbymeansofanintermediarykinematicschain(Figs.3±5).FurtherpossibilitiesareshowninRefs.[2±7].Fig.2I.Simionescu,L.Ciupitu/MechanismandMachineTheory35(2000)1287±12981289Fig.3showsakinematicsschemainwhichlink2isjoinedwiththeframeatpointC,anditisdrivenbymeansoftheconnectingrod3fromtherobotarm1.Thebalancingoftheforcessystemthatactsonthearm1isexpressedbythefollowingequation:fiˆÿm1OG1cosji‡m4AXA
g‡Fs…YAcosyiÿXAsinyi†‡R31XYEÿR31YXEˆ0,iˆ1,...,12,…2†where:yiˆarctanYBÿYAXBÿXA;m4