Design and analysis of kinematically redundant planar parallel manipulator for isotropic stiffness condition

Abstract

Parallel manipulators are a form of closed loop linkages and have a wide range of applications e.g. surgical robots, flight simulators, pointing devices etc. Parallel mechanisms have many advantages over serial manipulator. Higher accuracy, stiffness and increased payload capacity are the characteristics of parallel manipulator. In spite of many advantages, they have limited workspace and more singularity regions. So, redundant architectures have become popular. However, redundancy leads to infinite solutions for inverse kinematic problem. The current work addresses this issue of resolving the redundancy of kinematically redundant planar parallel manipulators using optimization based approach. First the conventional non-redundant 3-RPR planar parallel manipulator is presented. Afterwards the kinematically redundant counterpart 3-PRPR is discussed and actuation redundant 4-RPR has been touched upon briefly. Computer simulations have been performed for the kinematic issues using MATLAB programme . The workspace of redundant and non-redundant parallel manipulators have been obtained. The generalized stiffness matrix has been derived based upon the Jacobian model and the principle of duality between kinematics and statics. A stiffness index has been formulated and the isotropy of stiffness index is used as the criterion for resolving redundancy. A novel spiral optimization metaheuristics has been used to achieve the isotropic stiffness within the selected workshape and the results are compared against particle swarm optimization. The results obtained from the novel Spiral optimization are found to be more effective and closer to the objective function as compared to the particle swarm optimization. Optimum redundant parameters are obtained as a result of the analysis. A wooden skeletal prototype has also been fabricated to enhance the understanding of the mechanism workability.