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。
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.
作者
耿明超
边辉
张灿果
李欣
Geng Mingchao1,Bian Hui2,Zhang Canguo1,2,Li Xin1(School of Mechanical Engineering,Hebei University of Architecture,Zhangjiakou 075000,China;2.Hebei Provincial Key Laboratory of Parallel Robot and Mechatronic System,Yanshan University,Qinhuangdao 066004,Chin)
出处
《机械传动》
CSCD
北大核心
2018年第5期67-72,共6页
Journal of Mechanical Transmission
基金
河北省自然科学基金(E2018404044
E2015203144)
河北省高等学校青年拔尖人才计划项目(BJ2016017)
国家自然科学基金(51305380)
张家口市科技计划项目(1621009B)
河北建筑工程学院校基金(B-201603)
关键词
并联机构
正解
迭代搜索
拟牛顿
Parallel mechanism
Forward kinematics
Iterative search Quasi - Newton
