Time efficient stiffness model computation for a parallel haptic mechanism via the virtual joint method

Haptic devices are used for displaying a range of mechanical impedance values to the user. This impedance is regulated by a real-time control loop depending on the position information of the end-effector, which is usually acquired indirectly by using forward kinematics equations. Nevertheless, the kinematic model is insufficient to obtain accurate values if there are non-negligible compliant displacements. This gives a strong motivation for implementing a real-time stiffness model in the haptic control loop for improving its accuracy. Additionally, stiffness performance indices can be used at the design stage for enhancing the haptic devices impedance range within optimal design procedures. Fast solutions of a stiffness model are required for a real-time control as well as for decreasing the optimization time during a design process with a trade-off between accuracy and computational costs. In this study, we propose a computation time-efficient stiffness analysis of a parallel haptic device mechanism. The accuracy and computational costs of the proposed model are calculated and compared with a model that is obtained via a finite element method to demonstrate the effectiveness of the proposed approach with the desired real-time and accuracy performance.