Formulating an invariant manipulability index of Gough-Stewart platform

Manipulability indexes have been extensively used as objective functions or constraints in the optimal design of robots, especially for the robots with pure active joints and the end-effectors only involving positioning or orientation. The moving platform of Gough-Stewart platform can involve both positioning and orientation, which leads to the conventional Jacobian matrix with entries bearing disparate physical units, then the established manipulability index based on the conventional Jacobian matrix has no physical meaning and is variable under a change of units. Based on a dimensionless Jacobian matrix, this paper established a new manipulability index, which has physical meaning and is invariant under a change of units. In order to design a good performance motion simulator, the extreme values of the new and old manipulability indexes of 2 commercial flight simulators in their reachable workspaces were found by random search method, respectively. From the results, the extreme values of the new manipulability index are in regularity, and can be used as references in the optimal design of the Gough-Stewart platform as motion simulator.