Coupled dynamics of flexible cables and rigid end-effector for a cable suspended robot

An important application of cable-suspended robots is in long-reach manipulation tasks. The usual assumption of rigid cables is not valid in these situations. The flexibility of cables needs to be included during modeling of residual motion of the manipulator after a gross motion has been made. In this paper, we assume that a gross motion has already been made that brings the end-effector to its desired position. Vibrations still persist due to flexibility in cables about this desired configuration. The paper provides a model to relate the position and rotation of the end-effector and the input including the flexible cable dynamics. The derived input-output model for the system is a set of delay-differential equations. We then apply the delta flatness theory to calculate the control inputs applied by the actuators at the end of the ropes for given trajectories for the six degrees-of-freedom of the system. The approach is illustrated by mathematical simulation in this paper