Forward kinematic solution through geometry analysis for rehabilitation cable robot

We have an interest in the forward kinematic solution of a three-DOF cable-driven parallel end effecter for rehabilitation of the upper limbs. Although to solve the forward kinematic solution is to decide the position and orientation of end effecter by using four given cable lengths, it is well known that it is difficult to make sure the only solution among multiple solutions of cable-driven parallel end effecter because of the lack of given information. Through the geometry analysis, we newly found that the orientation of end effecter can be estimated from intersection points of four circles drawn by four given cables. Accordingly, we prove that the position and orientation for the only solution can be easily decided by our new proposal method without the extra sensory system and the calculation of complicated non-linear equation.