Wire-actuated robot manipulators are generally lighter than other manipulators as actuated wires are used instead of joint actuators. The inverse dynamic modeling of these manipulators is complicated by the existence of multiple kinematic constraints as well as redundancy in actuation. In wire-actuated parallel manipulators with a constraining linkage and in tendon-driven serial manipulators, wires are used to control the joints. In these manipulators, each wire can provide a torque/force on a link about/along its revolute/prismatic passive joint in one direction, as wires only act in tension. Using one wire for each link sometimes does not fully constrain the motion of the link about/along its passive joint. Therefore, a second wire is attached to some links in a “counterbalance” configuration; i.e., the second wire can provide a “complementary” torque/force in the opposite direction of the torque/force produced by the first wire on the link about/along its passive joint. Depending on the end effector trajectory and external force at each instant, one of the mentioned two wires provides the desired direction of torque/force and the other, “counteracting wire,” imposes a “counteracting” torque/force on the link about/along its passive joint. Using more actuators than degrees of freedom (DOF) in the manipulator causes redundancy in actuation, which means that for a unique end effector trajectory and external force, inverse dynamic results (actuator torques/forces) have infinite solutions within a null space of actuator torques/forces. Obtaining a unique result within the null space requires several considerations, such as avoiding negative tensions in wires and decreasing the actuator torques/forces. The purpose of this article is to find a methodology to limit the infinite inverse dynamic solutions to one while the negative wire tensions are avoided and actuator torques/forces are relatively decreased. As explained in this article, by reducing the counteracting wire tensions, other actuator torques/forces are decreased, because a portion of other actuator torques/forces neutralizes the tensions of counteracting wires. A methodology is developed to detect the counteracting wires in real-time and to present the corresponding tensions to a low positive value; i.e., the counteracting wires are “deactivated.” The proposed methodology can be implemented in the inverse dynamic modeling of wire-actuated parallel manipulators with a constraining linkage and tendon-driven serial manipulators via using the Lagrangian method. This methodology can be used to provide optimum actuator torques/forces and avoid negative tensions in actuated wires. The methodology is implemented in the inverse dynamic modeling of a 4-DOF wire-actuated manipulator where there is one degree of actuation redundancy. In the simulation results, the inverse dynamic model based on the proposed methodology is observed to be quite robust in terms of avoiding negative wire tensions by deactivating the right actuated wire.
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