Workspace Envelope Formulation of Planar Wire-actuated Parallel Manipulators

In this article, the workspace of planar wire-actuated parallel manipulators is studied. The investigation is based on two methods: an analytical method which formulates the workspace envelope by means of Cramer’s rule pertaining to the Jacobian matrix and the null space method from static analysis of manipulator. The workspace envelope method is extended to analyzing redundant planar manipulators and planar manipulators with an external wrench or gravity modelled as an additional wire. It is discussed that the null space method gives a more realistic workspace formulation as it takes into account wire tension limits, while the workspace generated by the workspace envelope method assumes very large wire tensions are possible. The workspace envelope method plots an analytical function as the border of the workspace so a much higher resolution representation of the wrench closure workspace is possible.