Unified Kinematics and Singularity Analysis of a Metamorphic Parallel Mechanism With Bifurcated Motion
Unified Kinematics and Singularity Analysis of a Metamorphic Parallel Mechanism With Bifurcated Motion
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DOI：
10.1115/1.4024292
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发表时间：
2013-08
期刊：
影响因子：
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通讯作者：
D. Gan;J. Dai;J. Dias;L. Seneviratne
中科院分区：
文献类型：
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作者：
D. Gan;J. Dai;J. Dias;L. Seneviratne
介绍了一种由四个可重构rTPS分支组成的新型变胞并联机构。基于可重构Hooke关节的可重构性，将rTPS肢体分为两个阶段，在一个阶段，肢体对平台没有约束，在另一个阶段，它约束球关节中心位于一个平面上。这导致该机制具有在具有可变移动性的不同拓扑之间重新配置的能力。基于点-平面约束建立了平台转动矩阵和平移矢量的几何约束方程，揭示了导纳为2的拓扑结构的运动分叉特性和变换为其它拓扑结构时导纳变化的几何条件。在此基础上，提出了一种统一的运动学肢体建模，考虑到可重构rTPS肢体的两个阶段之间的差异。这是进一步应用于机构建模和逆运动学和正运动学的解析求解相结合的四肢覆盖所有的机构拓扑结构。在此基础上，通过定义雅可比矩阵中的几何约束力和驱动力及其在可变拓扑结构中的变化，提出了一种统一的奇异性建模方法。利用该模型对具有奇异性分布的工作空间进行了分析，得到了相应的奇异轨迹，并对特殊的奇异位形进行了说明。[DOI 10.1115/1.4024292]
This paper introduces a new metamorphic parallel mechanism consisting of four reconfigurable rTPS limbs. Based on the reconfigurability of the reconfigurable Hooke (rT) joint, the rTPS limb has two phases while in one phase the limb has no constraint to the platform, in the other it constrains the spherical joint center to lie on a plane. This results in the mechanism to have ability of reconfiguration between different topologies with variable mobility. Geometric constraint equations of the platform rotation matrix and translation vector are set up based on the point-plane constraint, which reveals the bifurcated motion property in the topology with mobility 2 and the geometric condition with mobility change in altering to other mechanism topologies. Following this, a unified kinematics limb modeling is proposed considering the difference between the two phases of the reconfigurable rTPS limb. This is further applied for the mechanism modeling and both the inverse and forward kinematics is analytically solved by combining phases of the four limbs covering all the mechanism topologies. Based on these, a unified singularity modeling is proposed by defining the geometric constraint forces and actuation forces in the Jacobian matrix with their change in the variable topologies in terms of constraint screws. Analysis of workspace with singularity distribution is carried out using this model and corresponding singularity loci are obtained with special singular configurations illustrated. [DOI: 10.1115/1.4024292]