Forward Kinematics Analysis of 2RUS/RRS Parallel Mechanism

Geng Mingchao; Bian Hui; Zhang Canguo; Li Xin

doi:10.16578/j.issn.1004.2539.2018.05.013

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Forward Kinematics Analysis of 2RUS/RRS Parallel Mechanism

更新时间：2022-10-20

- Forward Kinematics Analysis of 2RUS/RRS Parallel Mechanism
- Vol. 42, Issue 5, Pages: 67-72(2018)
- 作者机构：
  
  1. 河北建筑工程学院机械工程学院
  2. 燕山大学河北省并联机器人与机电系统实验室
- 作者简介：
- 基金信息：
- DOI：10.16578/j.issn.1004.2539.2018.05.013
  CLC：
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[1]耿明超,边辉,张灿果,李欣.2RUS/2RRS并联机构位置正解分析[J].机械传动,2018,42(05):67-72.

Geng Mingchao, Bian Hui, Zhang Canguo, et al. Forward Kinematics Analysis of 2RUS/RRS Parallel Mechanism. [J]. 42(5):67-72(2018)
[1]耿明超,边辉,张灿果,李欣.2RUS/2RRS并联机构位置正解分析[J].机械传动,2018,42(05):67-72. DOI： 10.16578/j.issn.1004.2539.2018.05.013.

Geng Mingchao, Bian Hui, Zhang Canguo, et al. Forward Kinematics Analysis of 2RUS/RRS Parallel Mechanism. [J]. 42(5):67-72(2018) DOI： 10.16578/j.issn.1004.2539.2018.05.013.

摘要

迭代搜索算法（牛顿法或拟牛顿法）是求解并联机构位置正解的重要方法。由于分支的极限位置奇异,迭代搜索算法的搜索空间易于超出机构的工作空间,导致其在求解2RUS/2RRS这一类并联机构位置正解时失效。以平面串联分支为例,给出了具有一定通用性的消除分支极限位置奇异的等效方法,并将2RUS/2RRS机构等效为2UPS/2RPS机构进行正解求解。基于动平台转动角速度和欧拉角导数的关系,通过虚设机构法得到了等效机构4×4的雅可比矩阵。将初始位姿对应等效机构雅可比矩阵作为每次迭代的近似初值,能够进一步减少拟牛顿法的计算量,提高计算效率。最后,采用拟牛顿法中的逆Broyden算法对2RUS/2RRS机构的正解进行了数值验证。

Abstract

The iterative search method（ Newton or Quasi-Newton） is an important numerical method for solving the forward kinematics（ FK） problem of parallel mechanisms. Due to the extremely displacement singularity in the limbs,the search space is easy to be out of the mechanism workspace,which causes failed in solving the FK problem of the class of 2 RUS/2 RRS mechanism. Taking the plane series branch as an example,the equivalent method of eliminating the extremely displacement singularity is given,and the 2 RUS/2 RRS mechanism is equivalent to a 2 UPS/2 RPS mechanism. Based on the relationship between the angular velocity and the Euler’s derivative,the 4 × 4 Jacobian matrix is gotten through the virtual mechanism method. The Jacobian matrix of the initial pose of the equivalent mechanism can be taken as the approximate initial value of the Quasi-Newton method,which can reduce the calculation and improve the computational efficiency. The FK problem of 2 RUS/2 RRS are numerically verified by inverse Broyden algorithm in Quasi-Newton method.

关键词

并联机构正解迭代搜索拟牛顿

Keywords

Parallel mechanismForward kinematicsIterative searchQuasi-Newton

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