In consideration of the second-order coupling quantity of the axial displacement caused by the transverse displacement of flexible beam, the first-order approximation coupling model of planar 3-RRR flexible parallel robots is presented, in which the rigid body motion constraints, elastic deformation motion constraints, and dynamic constraints of the moving platform are considered. Based on the different speed of the moving platform, numerical simulation results using the conventional zero-order approximation coupling model and the proposed firstorder approximation coupling model show that the effect of “dynamic stiffening” term on dynamic characteristics of the system is insignificant and can be neglected, and the zero-order approximation coupling model is enough precisely for catching essentially dynamic characteristics of the system. Then, the commercial software ANSYS 13.0 is used to confirm the validity of the zero-order approximation coupling model. 1. Introduction In recent several decades, many researchers have paid more attention to the light flexible robots with high-speed, high-acceleration, and high-precision which are widely used in the assembly industry, the aerospace industry and the precision machining, and the measurement field. Essentially, the flexible parallel robots mechanism belongs to flexible multibody system. Dynamic modeling of flexible multibody system is a challenging task, in which not only rigid-flexible coupling effect must be studied but also elastic deformation coupling must be analyzed carefully. At present, dynamic modeling and control of the flexible multibody system have received considerable attention as seen in survey papers [1–4]. Unfortunately, most of published works in this area addressed the manipulators with one flexible link. Comparing with single-link flexible manipulator, two-link flexible manipulator, or four-bar linkage flexible mechanism [5, 6], the research works on the flexible parallel robots are rather few. Recently, few works have been done on dynamic modeling and control of complex mechanisms. Lee and Geng [7] developed a dynamic model of a flexible Stewart platform using Lagrange equations. Wang et al. [8–10] studied dynamic modeling and control of planar 3-Prismatic-joint-Revolute-joint-and-Revolute-joint (3-PRR) parallel robots. Zhang et al. [11, 12] studied dynamic modeling method and dynamic characteristics of planar 3-RRR flexible parallel robots. Q. H. Zhang and X. M. Zhang [13] also studied dynamic performance of planar 3-RRR flexible parallel robots under uniform temperature change. For a
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