In this study, the effect of active joint failure on the mobility, velocity, and static force of parallel robot manipulators is investigated. Two catastrophic active joint failure types are considered: joint jam and actuator force loss. To investigate the effect of failure on mobility, the Gru¨bler’s mobility equation is modified to take into account the kinematic constraints imposed by various branches in the manipulator. In the case of joint jam, the manipulator loses the ability to move and apply force in a specific portion of its task space; while in the case of actuator force loss, the manipulator gains an unconstrained motion in a specific portion of the task space in which an externally applied force cannot be resisted by the actuator forces. The effect of joint jam and actuator force loss on the velocity and on the force capabilities of parallel manipulators is investigated by examining the change in the Jacobian matrix, its inverse, and transposes. It is shown that the reduced velocity and force capabilities after joint jam and loss of actuator force could be determined using the null space vectors of the transpose of the Jacobian matrix and its inverse. Computer simulation is conducted to demonstrate the application of the developed methodology in determining the post-failure trajectory of a 3-3 six-degree-of-freedom Stewart-Gough manipulator, when encountering active joint jam and actuator force loss.
Task Space Trajectory Tracking Control of Robot Manipulators with Uncertain Kinematics and Dynamics