An Algorithm to Study the Elastodynamics of Parallel Kinematic Machines with Lower Kinematic Pairs

In this paper an algorithm to help designers to integrate the elastodynamics analysis along with the inverse positioning and orienting problems of a parallel kinematic machine (PKM) into a single package is conceived. The proposed algorithm applies concepts from the Matrix Structural Analysis and FEA to determine the generalized stiffness matrix and the linearized elastodynamics equations of a PKM with only lower kinematic pairs. A PKM is modeled as a system of flexible links and rigid bodies connected by means of joints. Three cases are analyzed to consider the combinations between flexible and rigid bodies in order to find the local stiffness matrices. The latter are combined to obtain the limb matrices and, then, the global stiffness matrix of the whole robotic system. The same nodes coming from the links discretization are considered to include joint masses/inertias into the model. Finally, a case study is proposed to show some feasible applications and to compare results to commercial software for validation.