Optimum Layouts for Wire-actuated Parallel Manipulators Considering Their Stiffness Characteristics and Wire Failure

In this paper, stiffness of planar translational wire-actuated parallel manipulators is studied. The complete form of the stiffness matrix of the two degrees of freedom manipulators is formulated parametrically. The differential form of the static force balance equations is used to incorporate the variation of wire stiffness with wire length and the change in the Jacobian matrix under external force in the stiffness model. Failure of a wire, for the cases that the wire is disconnected or slack, as well as reconfiguring the anchor positions are investigated and their effects on the workspace of manipulators are presented while satisfying the constraints on wire tension and minimum stiffness. The stiffness characteristics of an example manipulator, before and after a wire failure, are discussed. Optimum layouts of the manipulator, by reconfiguring the positions of wire anchors, are identified to maximize the area of the stiffness maps.