3-RPS并联机构运动与静力特性分析-郑魁敬

28920119JOURNALOFMACHINEDESIGNVol．28No．9Sep．20113-RPS*0660043-RPS。3-RPSTH122A1001－2354201109－0028－06、、1－3。Hunt43-RPS。53-RPS63-RPS73-RPS83-RPS93-RPS103-RPS。113-RPS123-RPS133-RPS143-RPS。3-RPS。13-RPS3-RPS1、、3RPS－－。RPS3P。13-RPS23-RPS2．113-RPS△S1S2S3、BXBOBS1△R1R2R3AXAOAR1。△R1R2R3rAR1R2R3AAPRi△S1S2S3*2010－09－072011－03－09E20090003871971—、20。rBS1S2S3BBPSi。XYZABT=cβcγ－cβsγsβAXbosαsβcγ+cαsγ－sαsβsγ+cαcγ－sαcβAYbo－cαsβcγ+sαsγcαsβsγ+sαcγcαcβAZbo00011s———sinc———cos。3ALiLi=ABTBPSi－APRi=ABRBPSi+APbo－APRii=12322．23-RPS333AXbo=rB2cosβcosγ+sinαsinβsinγ－cosαcosγAYbo=rBcosβsinγγ=－arctansinαsinβcosα+cosβ336AZboαβγAXboAYboαβ。33-RPS3．11AVboOBAωbArSiSiOBAVSiSiAniLiuiRil·iLii=123。SiAVSiAVSi=AVbo+Aωb×ArSi4AVSiuiAVui=00=AVSi·Aui=AuTiArSi×AuiTAVboAω[]b530=JuAAVboAω[]b6JuA———JuA=AuT1ArS1×Au1TAuT2ArS2×Au2TAuT3ArS3×Au3T。l·iAVSiLil·i=AVSi·Ani=AnTArSi×AniTAVboAω[]b73L·=J1AAVboAω[]b8L·=l·1l·2l·3TJ1A———J1A=AnT1ArS1×An1TAnT2ArS2×An2TAnT3ArS3×An3T。58L·[]0=JAVboAω[]b9J———J=J1AJ[]uA。AVboAω[]b=J－1L·[]010J－1———。Aωb=10sinβ0cosα－sinαcosβ0sinαcosαcosβα·β·γ·1111AVboAω[]b=J2AAVboα·β·γ·123γ·=－α·sinβ+β·sinα1+cosαcosβAVxbo=rB2α·cosαsinβsinγ+sinαcosγ+β·sinαcosβsinγ－sinβcosγ+γ·sinαsinβcosγ+cosαsinγ－cosβsinγAVybo=rB－β·sinβsinγ+γ·cosβcosγ1392201193-RPS13AVboα·β·γ·=J3AVzboα·β·1412148L·=J'AVzboα·β·15J'A3×3———J'A3×3=J1AJ2AJ3A∈R3×3。J'A∈R3×3J－1A15Vzboα·β·=J'－1Al·1l·2l·316J'－1A3。。3．21113－sinβ1+cosαcosβAωbx+sinαcosβ1+cosαcosβAωby－Aωbz=01711、1317AVboAωbTAωbxAωbyAωbz3AVxboAVyboAVzboAVzboAVxboAVybo3。43-RPS4．1311f=f1f2f3T2fsr=fsr1fsr2fsr3T3FM。4．20∑3i=1nifi+uifsri+F=0∑3i=1rSi×nifi+rSi×uifsri+M={018－F－MT=GffsrT19G———G=n1n2n3u1u2u3rS1×n1rS2×n2rS3×n3rS4×u1rS5×u2rS6×u[]3。AG∈R6×6AG－1ffsrT=AG－1－AF－AMT203、3AGAG－1。4．31020G－1=J－T2121。53-RPS5．1D-H3S1S2S3AX1=rA－l1sinθ1AY1=0AZ1=l1cosθ{1AX2=－1/2rA－l2sinθ2AY2=槡3/2rA－l2sinθ2AZ2=l2cosθ{222AX3=－1/2rA－l3sinθ3AY3=－槡3/2rA－l3sinθ3AZ3=l3cosθ{303289liθii=1233。AXbo=－162l1sinθ1－l2sinθ2－l3sinθ3AYbo=－槡36l2sinθ2－l3sinθ3AZbo=－13l1cosθ1+l2cosθ2+l3cosθ323Y=0AXbo=－162l1sinθ1－l2sinθ2－l3sinθ3AYbo=－槡36l3sinθ3－l2sinθ2AZbo=13l1cosθ1+l2cosθ2+l3cosθ324Y=－槡3XAXbo=－162l3sinθ3－l1sinθ1－l2sinθ2AYbo=－槡36l2sinθ2－l1sinθ1AZbo=13l1cosθ1+l2cosθ2+l3cosθ325Y=槡3XAXbo=－162l2sinθ2－l1sinθ1－l3sinθ3AYbo=－槡36l1sinθ1－l3sinθ3AZbo=13l1cosθ1+l2cosθ2+l3cosθ32633liθii=1232－31－31－2Y=0Y=－槡3XY=槡3X3。5．2S1S2S3fxyz=Ax+By+Cz+D=0nBnB=nBXnBYnBZT=AA2+B2+C槡2BA2+B2+C槡2CA2+B2+C槡[]2T27A=槡32rA－l2sinθ2l3cosθ3－l1cosθ1+槡32rA－l3sinθ3l2cosθ2－l1cosθ1B=－123rA－l3sinθ3－2l1sinθ1l2cosθ2－l1cosθ1+123rA－l2sinθ2－2l1sinθ1l3cosθ3－l1cosθ1C=槡34rA－l3sinθ33rA－l2sinθ2－2l1sinθ1+槡34rA－l2sinθ23rA－l3sinθ3－2l1sinθ1127cosθX=nBX=sinβcosθY=nBY=－sinαcosβcosθZ=nBZ=cosαcos{β28α=－arctanB/Cβ=arcsinAA2+B2+C槡(){2293θ1θ2θ33l1l2l33、2329。66．1rA=0．2mrB=0．15mZmin=0.552mZmax=0．952mlimin=0．554mlimax=0.953m。23。a13201193-RPSb23-RPS6．2X0°～20°Y0°～20°Z0．552m～0．752m1s10s1s13。1t/sAVxbo/mm/sAVybo/mm/sAVzbo/mm/sAωbx/°/sAωby/°/sAωbz/°/s00000001－2．8×10－5－0．0914201．99942．00035．3×10－62－7．5×10－4－0．2737201．99452．00271．4×10－43－0．0035－0．4546201．98472．00766．6×10－44－0．0095－0．6333201．97012．01480．00185－0．0202－0．8088201．95052．02430．00396－0．0367－0．9802201．92582．03610．00717－0．0604－1．1465201．89622．04990．01178－0．0923－1．3066201．86142．06570．01799－0．1336－1．4595201．82142．08340．026110－0．1855－1．6039201．77612．10270．03641100000031317。6．310sX0°20°Y0°20°Z0．552m0．752mFM3f3fsr4。aF=521TM=343TbF=－10000TM=0－2．7412．5T4713-RPS3AVzboAωbxAωbyAωbz。233-RPSY=0Y=－槡3XY=槡3X。33-RPS。433。1．J．20065202－205．2．J．200945958－63．3．4－RPRRRJ．200623814－16．4HuntKH．Structuralkinematicsofin-parallel-actuatedro-23289bot-armsJ．JournalofMechanismsTransmissionsandAutomationinDesign198310512705－712．5．3-RPSJ．2001173239－242．6LiYanwenHuangZhen．Methodusedinsingularityre-searchbasedonkinematicsanditsexampleinapplicationJ．ChineseJournalofMechanicalEngineering2004172161－165．7．3-RPSJ．20072851210－1215．8．3-RPSJ．2008324299－303．9．3-RPSJ．201046124－28．10．J．200724828－29．11．3-RPSJ．200917171－73．12．3-RPSJ．2004424－26．13．J．2009622－25．14．3-RPSJ．2009369146－150．Kinematicsandstaticcharacteristicsanalysisof3-RPSparallelmechanismZHENGKui-jingCUIPeiGUOHai-junCollegeofMechanicalEngineeringYanshanUniversityQinhuangdao066004ChinaAbstractThekinematicsandstaticcharacteristicsof3-RPSparallelmechanismwasanalyzedandtheinversedisplacementandposeconstrainedequationswereestablished．Byanalyzingthefor-wardandinversevelocityofthemechanismthecorrelationequa-tionsofvelocitycomponentsweresolved．Throughestablishingtheforcebalanceequationandstatictransfermatrixthedualrelationbetweenvelocitymappingandforcemappingwasdetermined．Byprovingthesymmetryofitsworkspaceagoodposeinspectionap-proachwasproposedtosolvetheforwarddisplacementproblemef-fectively．Theanalyticresultswereverifiedbythenumericalexam-ples．Ithaslaidthetheoreticalbasisfortheoptimumdesignandcontrolplanningoftheparallelmechanism．Keywords3-RPSparallelmechanismkinematicsstaticsvelocitycorrelationFig4Tab1Ref14“JixieSheji”欍欍欍欍欍欍欍欍欍欍欍欍