平面3-RRR和3-PRR柔性并联机器人弹性动力学分析

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In this paper,first,a flexible link is transformed into several discrete beam elements by means of the finite element method.Then,the elastodynamic models of planar 3-RRR and 3-PRR flexible parallel robots are established based on the floating coordinate system and the Lagrange equation,in which the lumped mass and the lumped moment of inertia of each joint and the moving platform,along with the Coriolis inertia forces and the centrifugal forces of rigid motion,are taken into consideration.With these models,the dynamic characteristics of the two above-mentioned robot systems,including the natural frequency,the elastic displacement and angle of the mo-ving platform as well as the maximum stress of each flexible link,are compared.The results indicate that the dynamic performance of planer 3-RRR robot is superior to that of 3-PRR robot with the same parameters.The findings build up a theoretical foundation for the type selection of planar full 3-DOF flexible parallel robots.采用有限元法对柔性连杆进行离散,运用浮动坐标系、拉格朗日方程建立了平面3-RRR和3-PRR柔性并联机器人的弹性动力学模型,该模型考虑了关节、动平台的集中质量和集中转动惯量,以及刚体运动的科式力和离心力.基于所建立的弹性动力学模型,比较了两系统的动力学特性,包括系统的固有频率、动平台的弹性位移和弹性转角、各柔性连杆的最大应力.结果表明：在参数一致的情况下,平面3-RRR机器人的动力学性能优于3-PRR机器人.文中结论可为平面完全3自由度柔性并联机器人的选型提供理论依据.