Local Kinematic Analysis of Closed-Loop Linkages—Mobility, Singularities, and Shakiness
Local Kinematic Analysis of Closed-Loop Linkages—Mobility, Singularities, and Shakiness
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DOI：
10.1115/1.4032778
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发表时间：
2016-08
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影响因子：
--
通讯作者：
A. Müller
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文献类型：
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作者：
A. Müller
一个连杆机构的活动性是由其成员所受的约束决定的。几何约束定义的配置空间（c-空间）品种的几何实体，其中有限的流动性的链接编码。连杆机构的局部运动学分析的目的是从局部c-空间几何中推导出给定构型下连杆机构的有限自由度。本文提出了一种局部分析的方法。后者是一个代数簇近似的c-空间。它允许调查的流动性在定期以及奇异的配置。瞬时迁移率由约束决定，而不是由c-空间几何形状决定。抖动和欠约束连杆机构是突出的例子，表现出永久更高的瞬时比有限的自由度，即使在规则的配置。另一方面，运动学奇异性反映在瞬时自由度的变化中。一个c-空间奇点作为一个运动学奇点，但运动学奇点可以是c-空间的一个正则点。所提出的方法允许识别c-空间奇点。它还揭示了theith-order流动性，并允许分类的联系，过度约束和欠约束。该方法适用于一般的低副多环机构。它是计算简单，只涉及李括号（螺旋产品）的瞬时关节螺钉。本文还总结了连杆机构的有关运动现象。
The mobility of a linkage is determined by the constraints imposed on its members. The geometric constraints define the configuration space (c-space) variety as the geometric entity in which the finite mobility of a linkage is encoded. The aim of a local kinematic analysis of a linkage is to deduce its finite mobility, in a given configuration, from the local c-space geometry. In this paper, a method for the local analysis is presented adopting the concept of the tangent cone to a variety. The latter is an algebraic variety approximating the c-space. It allows for investigating the mobility in regular as well as singular configurations. The instantaneous mobility is determined by the constraints, rather than by the c-space geometry. Shaky and underconstrained linkages are prominent examples that exhibit a permanently higher instantaneous than finite DOF even in regular configurations. Kinematic singularities, on the other hand, are reflected in a change of the instantaneous DOF. A c-space singularity as a kinematic singularity, but a kinematic singularity may be a regular point of the c-space. The presented method allows to identify c-space singularities. It also reveals theith-order mobility and allows for a classification of linkages as overconstrained and underconstrained. The method is applicable to general multiloop linkages with lower pairs. It is computationally simple and only involves Lie brackets (screw products) of instantaneous joint screws. The paper also summarizes the relevant kinematic phenomena of linkages.