Redundant manipulators have potential advantages of using their degree(s) of redundancy to satisfy additional task(s). To achieve desirable performance criteria, various optimization techniques can be applied to redundant manipulators. In the work presented, the redundancy resolution of planar wire-actuated parallel manipulators is investigated at the kinematic and dynamic levels in order to perform desirable tasks while maintaining positive tensions in the wires. Local optimization routines are used in the simulations in order to minimize the norm of actuator forces/torques or to minimize the norm of the mobile platform velocity, subject to positive tension in the wires. This paper presents techniques to alter wire tensions, mobile platform trajectory, mobile platform velocity, and length rate of wires, in order to maintain positive wire tensions. The effectiveness of the presented approaches is studied through simulations of an example planar wire-actuated manipulator. The presented approaches can be utilized in the design of controllers, trajectory planning, and dynamic workspace analysis.

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In the work presented, the optimal trajectory planning in wire-actuated parallel manipulators in the presence of an obstacle is investigated. The kinematics and dynamics of a wire-actuated parallel manipulator considering the elasticity and damping effects of wires are described. The redundancy resolution of planar wire-actuated parallel manipulators is investigated at the torque level in order to perform desirable tasks to minimize the effect of impact, while maintaining positive tension in each wire. A local optimization routine is used in the simulation to minimize the tension in the wires while modifying the trajectory of the mobile platform and maintaining positive wire tensions. During collision, the tension in the wires is optimized to reduce the effect of impact, and after collision, the trajectory is modified and the wire tensions are minimized in order to avoid collision for the remainder of the trajectory. The effectiveness of the presented approach is studied through a simulation of an example planar wire-actuated manipulator.

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