平面3-RRR柔性并联机器人动力学建模与分析

Dynamic modeling and analysis of planar 3-RRR flexible parallel robots

轻型、高速、高精度柔性并联机器人在诸如电子装配、精密加工与测量、航空航天领域有着巨大的应用前景。研究了一类平面3-RRR柔性并联机器人。采用有限元法对柔性杆进行离散,运用浮动坐标系,拉格朗日方程以及虚功原理,建立了平面3-RRR柔性并联机器人的刚-弹耦合非线性动力学方程。该方程考虑了各关节和动平台的集中质量和集中转动惯量。详细研究了弹性运动坐标和刚体运动坐标约束关系。通过基于小变形假设的数值仿真计算,并和简化KED方法进行比较,结果表明系统刚体运动的科氏力和离心力以及变换矩阵的时变性对系统动力学特性有着至关重要的影响。

The light, high-speed, flexible parallel robots with high-precision are widely used in the industry, e.g. electronic as- sembly, precision machining and measurement, aerospace and so on. Planar 3-RRR flexible parallel robots are investigated in this paper. Dynamic model of planar 3-RRR flexible parallel robots was formed by the finite element method, the floating frame of reference, Lagrange equation and the principle of virtual work. The nonlinear dynamic equation with rigid-elastic cou- pling was established, in which lumped masses and moments of inertia of each joints and the moving platform were considered. The constraint relationship between elastic motion coordinates and rigid ones was studied in detail. According to numerical sim- ulations based on small deformation hypothesis and Comparisons of the proposed method with simplified KED one, it is shown that centrifugal and Coriolis forces of the rigid motion in the system, and time-varying characteristic of the transformation ma- trix give most important influences on dynamic characteristics of the system.