Forward kinematics analysis and experimental validation of a four-cable-driven under-constrained parallel mechanism

Taking the sinking winch mechanism as prototype, this paper studies the forward kinematics problem of a four-cable-driven under-constrained parallel mechanism. The tension states (slackness and tautness) and properties of the cables are incorporated into the forward kinematics model. We propose a new algorithm (named traversal algorithm) to solve the tensions in cables and the pose of platform, under the condition that only the lengths of four cables are known. The simulation and experimental results on forward kinematics demonstrate the effectiveness and correctness of the model and the traversal algorithm. The results of this paper can be used to evaluate the effect of the unequal cables' lengths to the tension distribution of cables and pose of the platform for sinking winch mechanism.