For Parallel Kinematic Mechanisms (PKMs) with kinematic redundancy, mechanism configurations with higher stiffness can be chosen during motion-trajectory planning. However, substantial computational resources would be required for this optimization problem, specifically, for the solution of the two intertwined sub-problems:​ (i) calculation of the dynamic stiffness of any considered PKM configuration, at a given task-space location, and (ii) searching for the PKM configuration with the highest stiffness at this location. Herein, the former sub-problem is addressed via a novel effective emulator to provide a computationally efficient approximation of the dynamic-stiffness function suitable for optimization.

The proposed method for emulator development identifies the mechanism’s structural modes in order to break down the high-dimensional stiffness function into multiple functions of lower dimension. Via extensive simulations, some of which are described herein, it is demonstrated that the proposed emulator can predict the dynamic stiffness of a PKM at any given configuration with high accuracy and at a low computational expense.