Simplified inverse dynamic models of parallel robots based on a Lagrangian approach

This paper proposes and analyzes some simplified dynamic modeling methods for parallel robots. The proposed methods are based on a Lagrangian approach where the key concept consists in simplifying the expression of the energy for robots, especially for the distal links. First, the slender link method is discussed, where the link energy is calculated from the endpoints’ velocities. Then, the commonly used equivalent point mass (EPM) method is analyzed. Since the EPM method uses point masses to replace links, the main problem is how to assign the values of point masses. According to the energy equivalence principle, some methods are proposed to solve the value-assigning problem. The derivations of the proposed methods are given, and the errors caused by each method are analyzed. Based on the error analyses, some simple approaches are introduced to improve the accuracy of the EPM methods. Inverse dynamic models of a spatial robot are established based on the proposed methods. Then, detailed comparisons and analyses of the different dynamic models are given to show that the proposed methods are simple and have relatively high accuracy.