Inertia Match of a 3-RRR Reconfigurable Planar Parallel Manipulator
Inertia Match of a 3-RRR Reconfigurable Planar Parallel Manipulator
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DOI：
10.3901/cjme.2009.06.791
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发表时间：
2009
影响因子：
4.2
通讯作者：
Shao;Zhufeng;Tang;Xiaoqiang;Chen;Xu;Wang;Liping
中科院分区：
文献类型：
--
作者：
Shao;Zhufeng;Tang;Xiaoqiang;Chen;Xu;Wang;Liping
并联机械手的惯量匹配是指并联机械手换算到各执行机构轴上的惯性载荷与执行机构转动惯量之比保持在合理的范围内。目前关于并联机械臂的研究较多，但很少提及并联机械臂的惯性参数和惯性匹配。本文重点研究3-RRR可重构平面并联机械臂的惯性特性。根据虚功原理推导的逆动力学公式，以代数形式得到了3-RRR平面并联机械臂在执行机构空间中的惯性矩阵。然后，通过统一惯性矩阵的维数并对对角元素进行平均，确定并联机械手的等效惯量，即并联机械手换算到各执行器轴上的惯性载荷。通过将3-RRR并联机械臂的惯量问题转化为串联多杆机械臂的惯量问题，证明了逆动力学推导的等效惯量的实用性。根据惯性方程的物理意义，机械臂分为三个部分。进一步分析了各部件对等效惯量的贡献及其在所需工作空间内的分布，表明在计算并联机构的等效惯量时不能忽略被动环节。最后完成了3-RRR可重构并联机构在三种配置下的惯量匹配，并选择了减速器。等效惯量计算和惯性匹配结果表明，惯性数学是并联机构设计的必要步骤，惯性参数对并联机构的动态性能影响很大。此外，本文提出的等效惯量和惯性匹配原理可广泛应用于并联机械臂的动力学分析和伺服电机选型。
Inertia match of the parallel manipulator means the ratio of the inertial load of the parallel manipulator converted to each actuator shaft and the moment of inertia of the actuator is kept within a reasonable range. Currently there are many studies on parallel manipulators, but few mention inertia parameters and inertia match of parallel manipulators. This paper focuses on the inertia characteristics of the 3-RRR reconfigurable planar parallel manipulator. On the basis of the inverse dynamic formulations deduced with the principle of virtual work, the inertia matrix of the 3-RRR planar parallel manipulator in the actuator space is obtained in algebraic form. Then, by unifying the dimension and averaging diagonal elements of the inertia matrix, the equivalent inertia of the parallel manipulator, which is the inertial load of the parallel manipulator converted to each actuator shaft, is determined. By transforming the inertia problem of the 3-RRR parallel manipulator into that of the serial multi-bar manipulator, the practicality of the equivalent inertia deduced by inverse dynamics is demonstrated. According to the physical meaning of the inertia equation, the manipulator is divided in to three parts. Further analysis is carried out on the contribution of each part to the equivalent inertia and their distributions in the required workspace, revealing that the passive links cannot ignored in calculating the equivalent inertia of the parallel manipulator. Finally, the inertia match for the 3-RRR reconfigurable parallel manipulator under three configurations is accomplished, and reducers are selected. The equivalent inertia calculation and the inertial match results illustrate that the inertia math is a necessary step to the design of the parallel manipulator, and inertia parameters dramatically affect dynamic performances of parallel manipulators. Besides, the equivalent inertia and inertial match principles, proposed in the paper, can be widely applied in the dynamic analysis and servomotors selecting for the parallel manipulator.