Stiffness analysis of a planar parallel manipulator with variable platforms

This work investigates the stiffness characteristics of a planar parallel manipulator with variable platforms. The stiffness model is established with shape variables of the base and mobile platforms based on the Jacobian matrix. By virtue of a nondimensionalization of the inhomogeneous stiffness matrix, two homogeneous submatrices are obtained. Upon which, two kinds of performance indices are derived to evaluate the manipulator's stiffness behaviors, one for translation and the other for rotation. Stiffness performance of the considered manipulator with three types of platforms, namely variable base platform, variable mobile platform and both variable base and mobile platforms, is analyzed. To validate the stiffness models, the established analytical models are compared with the FEA based evaluations. In order to find the configurations with the best global stiffness performance, stiffness optimization with consideration of shape variables is conducted with the particle swarm optimization algorithm. Finally, a case study of platforms' shape changing in stiffness adjustment is presented.