Path-planning of a hybrid parallel robot using stiffness and workspace for foot rehabilitation

Stiffness is one of the important parameters for estimating the performance of hybrid parallel robots as it is not constant throughout its workspace. The aim of this study is to provide an optimum path based on maximum stiffness within the workspace of a 9-degree-of-freedom hybrid parallel mechanism configuration, which includes nine linear actuators connecting one stationary and two moving platforms in series. The proposed robot is designed for ankle rehabilitation, where accurate and precise movement of lower extremities is required. The design takes advantage of two important characteristics of parallel robots: stiffness and workspace. The proposed methodology to determine the stiffness of hybrid robot in three single axes is based on calculation of position vector of each actuator in any particular pose, by considering the inverse kinematics of the system, in order to obtain the magnitude and direction of the applied forces. The results obtained from the workspace calculations have been compared with those of two standard parallel mechanisms including a 6-degree-of-freedom hexapod and a tripod with 3 degrees of freedom. The stiffness of the robot has been calculated in simulation and then compared with those of a developed prototype hybrid model in two different case studies.