Workspace Generation for Wire-Actuated Parallel Manipulators
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This thesis focuses on the methods and results of the workspace formulation of wire-actuated parallel manipulators. Four methods of workspace generation are studied. The null space method, based on the calculation of wire tensions, is used to formulate the workspaces of example manipulators. The results of this method are used to verify the results of the following methods. This thesis presents that the convex hull workspace formulation method, a geometric analysis of the manipulator’s Jacobian matrix, can be extended to manipulators that have an external wrench and/or gravity applied to the mobile platform. The convex hull method is applied to the example manipulators investigated with the null space method. The workspace envelope characterization, an analytical approach of defining the borders of the workspace using the formulation of the kernel of the manipulator’s Jacobian matrix, is applied to the example planar manipulators investigated with the previous methods. A new process, presented in this thesis, of identifying the contribution of each set of four wires/forces of a planar manipulator allows the workspace envelope characterization to be applied to redundant planar manipulators and planar manipulators that have an external wrench and/or gravity applied to the mobile platform. The discrete and analytical antipodal methods, based on theorems from multi-fingered grasping manipulators, are presented and applied to the example planar manipulators investigated with the previous methods. This research generalizes the use of these theorems, which determine wrench-closure poses of planar four-wire manipulators that share wire-connection points on the base or mobile platform, to the discrete and analytical workspace formulation of planar three-degree-of-freedom wire-actuated manipulators with no restrictions on the number of wires or the configuration of the manipulator. Comparing all methods investigated in this thesis, the null space method results in the workspace that takes into account the maximum and minimum wire tensions and is recommended for use in the design of both spatial and planar wire-actuated parallel manipulators. All the other methods presented in this thesis, have similar results when compared to the null space method but formulate the maximum workspace which assumes the wires can operate with very high to infinite wire tension.