并联机构不同正解间无奇异转换问题探讨

On the Non-singular Path between Different Forward Kinematic Configurations of Parallel Mechanisms

  • 摘要: 并联机构的正解具有多解性,以一种平面三自由度并联机构为例,研究了不同正解之间的无奇异连接路径问题.结合Innocenti发现的第一条无奇异路径,采用基于奇异曲面的图形化方法分析了正解构型在工作空间中的分布.发现了两个正解间的多条类似路径,这些路径形成了连接两个正解位形的近似于螺旋状的管道空间.首次发现了在其它的正解之间也存在着这样的非奇异路径.这些结果表明并联机构的奇异曲面及正解分布异常复杂,如果两个正解对应的雅可比矩阵行列式值异号,则一定不存在无奇异路径;如果同号,则还要根据奇异曲面来定.两个正解构型间无奇异路径的判定还最终依赖于对奇异曲面更为清楚的描述.

     

    Abstract: Parallel mechanisms have multiple forward kinematic configurations,and we analyze the non-singular paths between different configurations with a 3-DOF planar parallel mechanism as an example.With the first path discovered by Innocenti, the distribution of these configurations in the workspace is analyzed based on graphic mode of singular surface.A lot of paths are found between these two configurations and these paths form a helix-like piping region.It first claims that there also exist another two configurations with this kind of paths.The results show that the distribution of singular surface and forward kinematic configurations of parallel mechanisms is very complex.If two configurations have opposite determinant sign of Jacobian matrix,there mustn’t have non-singular paths,while for the same sign,it should also be decided according to singular surfaces.The decision rule of non-singular path existence between two forward kinematic configurations depends on more clear discription of singular surface eventually.

     

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