Establishment and analysis of a unified mathematical model of kinematics and dynamics of flexible parallel mechanisms

Abstract The conventional positive solution approach for determining the forward motion of the kinematic mechanism relies primarily on the outcomes of the inverse solution of motion, which is not universally applicable to flexible parallel mechanisms. Furthermore, the process of analyzing the natural frequency of parallel mechanisms is complex, cumbersome, and challenging. More importantly, the two models are independent, and there is no unified mathematical analysis model for flexible parallel mechanisms. Therefore, this paper establishes a unified mathematical model for kinematics and dynamics analysis of flexible parallel mechanisms through an improved multi-body system transfer matrix method. Taking the flexible 3-RPU planar mechanism and the space 2-RPU (2-UPS) space mechanism as examples, respectively, the forward motion solution of the mechanism was analyzed and its working space range and resonance frequency were solved. Finally, the calculation results are compared with the simulation results, and the feasibility and accuracy of the method are proved. Through this method, we can quickly solve the motion characteristics of the mechanism without relying on the results of the inverse solution of the mechanism, which provides suggestions for the precise control of flexible parallel mechanisms and also provides corresponding reference basis for the practical application of flexible parallel mechanisms.