六自由度运动方程计算.pdf

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1、机器人运动学分析一机器人齐次坐标系的建立D—H坐标图二机器人正运动学分析变量为转角n杆件偏距dn(mm)扭角n杆长ln(mm)(图示角度值)11(0)d1=01=90l1=022(90)d2=02=0l2=33(0)d3=03=90l3=044(0)d4=4=-90l4=055(0)d5=05=90l5=066(0)d6=06=0l6=0éCqn-SqnCanSqnSanlnCqnùêúSqCqCa-CqSalSqA=ênnnnnnnúnê0SaCadúnnnêúë0001ûéC10S10ùéC2-S20l2C2ùéC30S30ùêúêúêúS0-C0SC

2、0lSS0-C0A=ê11ú,A=ê2222ú,A=ê33ú,123ê0100úê0010úê0100úêúêúêúë0001ûë0001ûë0001û1éC40-S40ùéC50S50ùéC6-S600ùêúêúêúS0C0S0-C0SC00A=ê44ú,A=ê55ú,A=ê66ú,456ê0-10dúê0100úê0010ú4êúêúêúë0001ûë0001ûë0001û由连杆6开始,依次导出下列方程:éC6-S600ùêúSC005T=A=ê66ú66ê0010úêúë0001ûéC5C6-C5S6S50ùêúSC-SS-C04T=AA=ê5656

3、5ú656êSC00ú66êúë0001ûéC4C5C6-S4S6-C4C5S6-S4C6C4S50ùêúSCC+CS-SCS+CCSS03T=AAA=ê456464564645ú6456ê-SCSSCdú565654êúë0001û2T=AAAA63456éC(CCC-SS)-SSC-C(CCS+SC)+SSSCCS+SCSdù3456463563456463563453534êúêS3(C4C5C6-S4S6)+C3S5C6-S3(C4C5S6+S4C6)-C3S5S6S3C4S5-C3C5-C3d4ú=êS4C5C6+C4S6-S4C5S6+C4C6

4、S4S50úêúë0001û1T=AAAAA623456éC23(C4C5C6-S4S6)-S23S5C6-C23(C4C5S6+S4C6)+S23S5S6C23C4S5+S23C5l2C2+S23d4ùêúêS23(C4C5C6-S4S6)+C23S5C6-S23(C4C5S6+S4C6)-C23S5S6S23C4S5-C23C5l2S2-C23d4ú=êS4C5C6+C4S6-S4C5S6+C4C6S4S50úêúë0001û0T=AAAAAA6123456éC1[C23(C4C5C6-S4S6)-S23S5C6]+S1(S4C5C6+C4S6)C1[

5、-C23(C4C5S6+S4C6)+S23S5S6]-S1(S4C5S6-C4C6)C1(C23C4S5+S23C5)+S1S4S5C1(l2C2+S23d4)ùêúS1[C23(C4C5C6-S4S6)-S23S5C6]-C1(S4C5C6+C4S6)S1[-C23(C4C5S6+S4C6)+S23S5S6]+C1(S4C5S6-C4C6)S1(C23C4S5+S23C5)-C1S4S5S1(l2C2+S23d4)=êúêS23(C4C5C6-S4S6)+C23S5C6-S23(C4C5S6+S4C6)-C23S5S6S23C4S5-C23C5l2S2-

6、C23d4úêúë0001ûénxoxaxpxùêúnoap由正运动学方程T=0T=AAAAAA=êyyyyú可得66123456ênoapúzzzzêúë0001û2n=C[C(CCC-SS)-SSC]+S(CS+SCC)x123456462356146456n=-C(CS+SCC)+S[C(CCC-SS)-SSC]y146456123456462356n=CSC+S(CCC-SS)z23562345646o=C[-C(CCS+SC)+SSS]+S(CC-SCS)x123456462356146456o=-C(CC-SCS)+S[-C(CCS+SC)+S

7、SS]y146456123456462356o=-CSS-S(CCS+SC)z23562345646a=C(CCS+SC)+SSSx12345235145a=-CSS+S(CCS+SC)y14512345235a=-CC+SCSz2352345p=C(lC+dS)x122423p=S(lC+dS)y122423p=lS-dCz22423三机器人逆运动学分析éC1S100ùéC2S20-l2ùêúêú0010-SC00A-1=êúA-1=ê22ú12êS-C00úê0010ú11êúêúë0001ûë0001ûéC3S300ùéC4S400ùêúêú0010

8、00-1dA-1=êúA-1=ê4ú34êS-C00úê-SC00