Stiffness and mass optimization of parallel kinematic machine

It has long been a challenge to carry out the optimal design of parallel kinematic machine (PKM) simultaneously considering stiffness and mass performances. This paper proposes the stiffness and mass optimization of PKM by settling performance indices, constraint conditions based on parameter uncertainty and cooperative equilibrium among performances. Firstly, instantaneous energy-based stiffness indices and mass in motion are defined as objectives. Instead of computationally expensive numerical analysis, analytical mapping models between objectives and parameters are investigated to improve optimization efficiency. Then, considering the effects of parameter uncertainty resulted from manufacturing errors during construction, constraint conditions are formulated by probabilistic method. Based on particle swarm optimization (PSO), a multi-objective optimization is implemented. A group of solutions are obtained to flag as Pareto frontier that reflects the competitive features between stiffness and mass performances. A cooperative equilibrium searching method is proposed to find out the final solution. Finally, this optimization approach is exemplified and validated by a five degree-of-freedom (DoF) PKM. Although its mass increases 17.17%, the stiffness is nearly 3 times better than before optimization.