Configuration and singularity analysis of a parallel hip joint simulator based on the forward kinematics
Configuration and singularity analysis of a parallel hip joint simulator based on the forward kinematics
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基于正向运动学的并联髋关节模拟器的构形与奇异性分析
DOI：
10.1016/j.apm.2016.03.017
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发表时间：
2016-08
影响因子：
5
通讯作者：
Shan Xianlei
中科院分区：
文献类型：
--
作者：
Li Yang;Lodewijks Gabriel;Pang Yusong;Shan Xianlei
并联机器人奇异位形的识别通常采用几何方法或基于位姿参数的运动学原理。这些方法在涉及奇点避免的应用中具有局限性，例如根据输入参数进行运动规划。为了从输入参数的角度识别奇点，从而使奇点避免策略在实际应用中更加直接和有效，本文以3SPS+1PS并联髋关节模拟器为例，重点研究了奇点、位形空间和输入参数之间的关系。借助于Sylvester透析法消去法得到了正运动学的单变量形式的多项式方程，从而证明了机械手的单输入最多有8种位形。然后根据它们的分布将这些配置分为两种类型的空间。结果发现，在实际应用中，我们只需要关注基本位形空间，其中奇异轨迹退化为单一曲面。最后，证明了该奇异条件与单变量形式的投入产出方程在实数域上有重根时的奇异条件等价。从而得到了输入参数的奇异条件方程和输入参数在基本位形空间中的奇异轨迹。该研究为并联机器人的奇异避免，特别是基于输入参数的运动规划中的无奇异设计提供了新的视角。
The singularities of parallel manipulators are usually identified by geometrical methods or by the kinematic principles based on the pose parameters. The methods have limitations in applications that involve singularity avoidance, such as motion planning from input parameters. To identify a singularity from an input parameter point of view, which would make the singularity avoidance strategy more direct and more effective in practical applications, this paper focuses on the relationship between the singularities, the configuration spaces and the input parameters with a 3SPS+1PS parallel hip joint simulator selected to implement this approach. A univariate-form polynomial equation of the forward kinematics is obtained with the aid of the Sylvester dialytic method of elimination, therefore proving that the manipulator has at most eight configurations for a single input. The configurations are then divided into two types of spaces according to their distributions. It is discovered that in practice, we only need concern ourselves with the basic configuration spaces, where the singular loci degenerate into a single surface. Finally, the singular condition is proved to be equivalent to that when the univariate-form input–output equation has a repeated root in the real number field. Therefore, the singular condition equation of the input parameters and the singular loci of the input parameters in the basic configuration spaces are obtained. This study provides new insight into the singularity avoidance of a parallel manipulator, especially for the singularity-free design in the motion planning from input parameters.
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作者：
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DOI：
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发表时间：
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期刊：
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影响因子：
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