An approach for elastodynamic modeling of hybrid robots based on substructure synthesis technique

Parallel kinematic machines exhibit strong pose-dependent static and dynamic behaviors, which makes accurate and rapid compliance analysis over the entire workspace an important issue in the design optimization. This paper presents a general approach for elastodynamic modeling of parallel kinematic machines using substructure synthesis technique. Firstly, the whole system is decomposed into two groups of substructures, i.e. component substructures and joint substructures. Then, the degrees of freedom of component substructures are reduced using modal reduction technique, and joint substructures are modeled by virtual springs with contact stiffness between adjacent component substructures. Finally, two threads are merged at junction surfaces to offer the equations of motion of the system as a whole, allowing the static and dynamic performances to be rapidly predicted with sufficient accuracy. The dynamic model of a 5-DOF hybrid robot is developed using the proposed method and the computational results show that rigidity and lower mode natural frequencies over the workspace match well with those obtained by the full finite element analysis.