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Hybrid-model-based stiffness analysis of a three-revolute-prismatic-spherical parallel kinematic machine

旋转副 运动学 工作区 刚度 运动学图 结构工程 机床 螺旋理论 计算机科学 运动链 工程类 机械工程 人工智能 物理 经典力学 机器人 约束(计算机辅助设计)
作者
Jun Zhang,Yan Zhao,Hai W Luo
出处
期刊:Proceedings of the Institution of Mechanical Engineers, Part B: Journal of Engineering Manufacture [SAGE Publishing]
卷期号:231 (14): 2561-2576 被引量:5
标识
DOI:10.1177/0954405416634257
摘要

A three-revolute-prismatic-spherical parallel kinematic machine is proposed as an alternative solution for high-speed machining tool due to its high rigidity and high dynamics. Considering the parallel kinematic machine module as a typical compliant parallel mechanism, whose three limb assemblages have bending, extending and torsional deflections, this article proposes a hybrid modeling methodology to establish an analytical stiffness model for the three-revolute-prismatic-spherical device. The developed analytical model is further used to evaluate the stiffness mapping of the three-revolute-prismatic-spherical module over a given work plane which is then validated by experimental tests. The simulations and experiments indicate that the present hybrid methodology can predict the three-revolute-prismatic-spherical parallel kinematic machine’s stiffness in a quick and accurate manner. The solution for eigenvalue problem of the stiffness matrix leads to the stiffness characteristics of the parallel module including eigenstiffnesses and the corresponding eigenscrews as well as the equivalent screw spring constants. Based on the eigenscrew decomposition, the parallel kinematic machine is physically interpreted as a rigid platform suspending by six screw springs. The minimum, maximum and average of the screw spring constants are chosen as indices to assess the three-revolute-prismatic-spherical parallel kinematic machine’s stiffness performance. The distributions of the proposed indices throughout the workspace reveal a strong dependency on the mechanism’s configurations. At the final stage, the effects of some design parameters on system stiffness characteristics are investigated with the purpose of providing useful information for the conceptual design and performance improvement of the parallel kinematic machine.
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