Research of the Workspace Boundary Solving and Flexibility of 3-RRR Planar Parallel Robot

Cao Liya; Cui Jiankun; Song Yanan

doi:10.16578/j.issn.1004.2539.2016.08.009

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Research of the Workspace Boundary Solving and Flexibility of 3-RRR Planar Parallel Robot

更新时间：2022-10-20

- Research of the Workspace Boundary Solving and Flexibility of 3-RRR Planar Parallel Robot
- Vol. 40, Issue 8, Pages: 38-42(2016)
- 作者机构：
  
  1. 上海理工大学机械工程学院
- 作者简介：
- 基金信息：
- DOI：10.16578/j.issn.1004.2539.2016.08.009
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[1]曹丽亚,崔建昆,宋亚楠.3-RRR平面并联机器人工作空间边界求解和灵活性研究[J].机械传动,2016,40(08):38-42.

Cao Liya, Cui Jiankun, Song Yanan. Research of the Workspace Boundary Solving and Flexibility of 3-RRR Planar Parallel Robot. [J]. 40(8):38-42(2016)
[1]曹丽亚,崔建昆,宋亚楠.3-RRR平面并联机器人工作空间边界求解和灵活性研究[J].机械传动,2016,40(08):38-42. DOI： 10.16578/j.issn.1004.2539.2016.08.009.

Cao Liya, Cui Jiankun, Song Yanan. Research of the Workspace Boundary Solving and Flexibility of 3-RRR Planar Parallel Robot. [J]. 40(8):38-42(2016) DOI： 10.16578/j.issn.1004.2539.2016.08.009.

摘要

提出了求解平面并联机器人工作空间边界的基于迭代搜索法的圆周式搜索算法,并分析了其灵活性指标。通过对3-RRR平面机器人工作空间的分析,根据迭代搜索法,在判别方程存在逆解的条件下,以圆周式搜索算法确定一系列的边界点,所得结果与运用几何方法得到的结果一致。利用末端执行器上点的速度来表示机构的运动,得出了受限制的、量纲一致的雅可比矩阵,从而衡量平面并联机器人的灵活性,并借助于Matlab绘图,直观地反映了新的雅可比条件数在工作空间内的分布情况。根据所得的雅可比矩阵,可以得到更准确的灵活性指标。

Abstract

A circular search algorithm for solving the spatial boundary of the planar parallel robot is proposed which is based on the iterative search method,and its flexibility index is analyzed. A series of boundary points for the workspace of the 3- RRR planar robot are determined by using the circular search algorithm depending on the existence of the inverse solution of the system. The results are consistent with the results by using geometric method. The restricted,dimension consistent Jacobian matrix can be obtained by using the speed of the end effector to represent the movement of the mechanism,which can measure the flexibility of the planar parallel robot,and with help of the Matlab graphics,the new Jacobi condition number distribution in the working space is intuitively reflected. According to the obtained Jacobian matrix,the more accurate flexibility indexes can be got.

关键词

并联机器人工作空间圆周式搜索算法灵活性雅可比矩阵

Keywords

Parallel robotWorkspaceCircular search algorithmFlexibilityJacobian matrix

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