吉林大学学报(工学版) ›› 2019, Vol. 49 ›› Issue (6): 1977-1985.doi: 10.13229/j.cnki.jdxbgxb20180636

• • 上一篇    下一篇

新的6⁃PSS型并联机构正向运动学求解方法

谢志江1(),王昆1,皮阳军1,吴小勇2,郭映位1   

  1. 1. 重庆大学 机械传动国家重点实验室, 重庆 400044
    2. 重庆理工大学 机械工程学院, 重庆 400054
  • 收稿日期:2018-06-19 出版日期:2019-11-01 发布日期:2019-11-08
  • 作者简介:谢志江(1963-),男,教授,博士生导师.研究方向:机械设计,机器人创新设计与控制.E-mail:xie@cqu.edu.cn
  • 基金资助:
    国家自然科学基金项目(U1530138)

Novel method for forward kinematics of 6⁃PSSparallel manipulator

Zhi-jiang XIE1(),Kun WANG1,Yang-jun PI1,Xiao-yong WU2,Ying-wei GUO1   

  1. 1. State Key Laboratory of Mechanical Transmission, Chongqing University, Chongqing 400044, China
    2. College of Mechanical Engineering, Chongqing University of Technology, Chongqing 400054, China
  • Received:2018-06-19 Online:2019-11-01 Published:2019-11-08

摘要:

针对6-PSS型并联机构,通过研究其正向运动学,利用各支链铰点在动坐标系、静坐标系和滑块铰点坐标系3种坐标系下的位置关系,推导出6-PSS型并联机构的运动学模型,得到一种简明的运动学正向求解方法。在此基础上,提出了基于多元牛顿法和最速下降法的组合数值方法,并运用数值分析理论和计算机机器算数思想,最大限度提高收敛速度和减少单步迭代计算量。最后,编制了机构运动学的正向求解程序,进行了数值仿真,结果表明:改进的组合数值方法不仅可以更加快速地收敛到真实解,还能降低对初始估计值的依赖,扩大收敛范围,可以有效应用于该型并联机器人系统。

关键词: 机械设计, 6-PSS型并联机构, 运动学正解, 多元牛顿法, 最速下降法, 组合数值方法

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

中图分类号: 

  • TH113

图1

6?PSS并联机构结构简图"

图2

初始状态下动、静平台铰点布置图"

图3

最速下降法程序流程图"

图4

迭代算法切换示意图"

表1

6?PSS机器人结构参数表"

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

表2

部分点的仿真结果统计表"

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

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
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
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
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
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