Dynamic modeling and analysis of a rigid-flexible planar parallel manipulator

In this paper, a method is presented for the dynamic modeling of parallel robots with flexible links and rigid platform. For a 3-RRR planar parallel manipulator, it is divided as three flexible sub-structures and a rigid moving platform. Because flexible sub-structures are connected by the rigid platform, the geometrical constraint relationship between them represent the influences each other. It is essential to obtain a simple displacement and dynamic relation between them. The flexible sub-structures are modeled by using floating-frame reference method, in which the coupling terms between the rigid-body motion and the flexible deformations and the geometric stiffness term are taken into account. According to the constraint relations, dynamic equations of the rigid platform are obtained. Finally the system dynamic equations can be obtained by assembling all dynamic equations. The displacement and orientation errors of the moving platform are analyzed in different case through numerical simulation. The results show the speed and structural size of the system have significant effects on the errors of the moving platform and the errors are different in different configuration of the manipulator.