新的6⁃PSS型并联机构正向运动学求解方法

doi:10.13229/j.cnki.jdxbgxb20180636

Abstract

Abstract:

Through the research of 6-PSS parallel manipulator, this paper developed the kinematics model based on the relationship between spherical joints' spatial positions in three kinds of coordinate systems, which respectively are the global coordinate system, the local coordinate system and the hinge-point coordinate systems fixed on sliding blocks. A composed numerical method based on multivariate Newton's method and the steepest descent method was proposed. The theories of numerical analysis and machine computation were used to improve the convergence speed and decrease the amount of operations in a single-step iterative process. Finally, the forward kinematics solution program was written for the numerical simulation. The results show that the improved composed numerical method can not only decrease the computational time and converge to the solution accurately, but also reduce the dependence on the initial estimate and expand the convergence range. This method can be effectively applied in robot system based on 6-PSS parallel manipulator.

Key words: mechanical design, 6-PSS parallel manipulator, forward kinematics solution, multivariate Newton's method, the steepest descent method, composed numerical method

CLC Number:

TH113

Zhi-jiang XIE,Kun WANG,Yang-jun PI,Xiao-yong WU,Ying-wei GUO. Novel method for forward kinematics of 6⁃PSSparallel manipulator[J].Journal of Jilin University(Engineering and Technology Edition), 2019, 49(6): 1977-1985.

Figures/Tables 6

Fig.1

Fig.2

Fig.3

Fig.4

Table 1

Structure parameters of 6?PSSparallel mechanism"

$l$ /mm	$r a$ /mm	$r b$ /mm	$? a$	$φ a$	$? b$	$φ b$
1 000	500	250	$π / 2$	$π / 6$	$π / 2$	$π / 6$

Table 1

Table 2

Simulation results of some points"

序号	输入量 $Δ i (i = 1,2, …, 6)$ /mm	最速下降法迭代次数	多元牛顿法迭代次数	组合方法总时间/s	组合方法输出 $α, β, γ, x c, y c, z c$ $/ (r a d ? ? ? ? ? ? o r ? ? ? ? ? ? ? m m)$	单独牛顿法迭代次数	单独牛顿法总时间 /s	单独牛顿法输出 $α, β, γ, x c, y c, z c$ $/ (r a d ? ? ? ? ? ? o r ? ? ? ? ? ? ? m m)$
1	-52.978，75.410， 126.710，47.602， -12.726，-35.234	无	无	无	无	5	0.001 74	0.100 000，0.199 999， 0.299 998，60.001 5， 39.998 6，20.000 0
2	-42.318，194.962， 332.980，168.590， 27.590，60.318	1	5	0.001 83	0.400 008，0.299 999， 0.700 001，199.999 5， 119.999 3，79.999 994	6	0.002 02	0.400 008，0.299 999， 0.700 001，199.999 5， 119.999 3，80.000 0
3	-14.826，222.002， 319.326，244.300， 127.828，179.708	2	5	0.001 92	0.700 001，0.400 001， 0.600 001，139.999 6， 200.001 5，119.999 4	7	0.002 11	0.700 001，0.400 001， 0.600 001，139.999 6， 200.001 5，119.999 4
4	-80.150，187.780， 310.226，160.274， 60.206，17.606	2	5	0.001 85	0.400 003，0.499 998， 0.699 999，100.000 4， 139.999 7，80.000 0	7	0.002 13	0.400 003，0.499 998， 0.699 999，100.000 4， 139.999 7，80.000 0
5	53.542，296.142， 475.294，401.766， 292.904，215.102	2	5	0.001 89	0.400 000，0.599 999， 0.500 003，159.999 776， 200.001 1，239.999 9	7	0.002 24	0.400 000，0.599 999， 0.500 003，159.999 8， 200.001 1，239.999 9
6	-46.182，212.540， 402.078，338.712， 184.406，140.414	2	5	0.001 93	0.599 998，0.600 002， 0.600 002，199.9998， 200.000 8，139.9996	7	0.002 16	0.599 998，0.600 002 0.600 002，199.999 8 200.000 8，139.999 6
7	-33.282，27.601， 171.838，517.644， 476.066，344.207	2	5	0.002 06	0.600 006，0.600 001 -0.499 998，209.998 5 240.000 9，149.999 8	不收敛	无	无
8	530.796，724.202， 152.260，-137.024， 186.516，727.426	6	5	0.002 95	0.799 996，-0.700 001， 0.999 999，-400.000 2， 250.001 0，120.000 0	不收敛	无	无
9	183.230，510.146， 951.193，822.089， 521.558，443.330	10	7	0.004 68	0.799 996，0.800 002， 0.999 998，400.000 4， 250.000 0，400.000 0	不收敛	无	无
10	-167.026，131.332， 533.602，835.502， 445.204，149.052	10	7	0.004 86	1.499 985，1.199 999， 0.999 989，360.001 4， 319.999 4，100.000 0	不收敛	无	无

Table 2

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Novel method for forward kinematics of 6⁃PSSparallel manipulator

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