The kinematics of the redundant $N-1$ wire driven parallel robot

We address the kinematics of the redundant $N-1$ wire-driven parallel robot, i.e. a robot with $N > 3$ wires connected at the same point on the platform. The redundancy allows one to increase the workspace size. But we show, both theoretically and experimentally that if the wires are not elastic, then the redundancy cannot be used to control the wire tensions. Indeed we show that whatever are the number of wires there will always be only at most 3 wires in tension, while the oth er $N-3$ wires will be slack. We then show that if the wires are elastic, then the platform positioning will be very sensitive to stiffness identification and wire lengths control. Hence classical redundant control schemes are difficult to use for such robot and alternate use of the geometry of redundant wires have to be considered.