Optimum kinematic design of a planar cable-driven parallel robot with wrench-closure gait trajectory

We report the design of a planar cable-driven parallel robot with four cables. The design can generate a wrench-closure trajectory of the lower limb, shank, with applications in gait rehabilitation. Using such a design, any external wrench on the target limb can be balanced using cables for all poses of the limb near to the trajectory in the gait cycle. We calculate the largest wrench-closure circular zone centered at an arbitrary point of the trajectory for a given range of orientations around a reference orientation of the limb. Taking the area of such zones into account for a set of points on a given trajectory, we optimize the robot kinematics with fixed cable attachment points. However, static evaluation of the robot in the trajectory indicates that, in some part of the trajectory, a general external wrench cannot be balanced. Therefore, a reconfigurable design of the robot is investigated in which the cable attachment points on the base can move with respect to the motion of the limb in its trajectory. The area of wrench-closure zones in the trajectory can be increased using different actuation schemes, which are obtained and compared. Finally, a redundant reconfigurable robot with an optimum wrench-closure gait trajectory is proposed.