Design of an antagonistically counter-balancing parallel mechanism

Much attention has not been paid to analysis of the open-loop stability for gravity counter-balancing of parallel mechanisms or closed-chain mechanisms. The open-loop stability is crucial especially in passively counter-balanced mechanisms where no actuators are involved. Passive hands-on device is such an example. A general stiffness model is derived for general closed-chain mechanism including counter-weight model. As a measure of the open-loop stability, we employ the determinant of the stiffness matrix. A parallel mechanism having 3 translational DOF (degree of freedom) is employed as an exemplary device. An antagonistically counter-balancing is found the most stable method. We conduct dynamic simulation and experiment to confirm the open-loop stability of the system.