An optimization approach to the determination of the boundaries of manipulator workspaces

An optimization approach to computing the boundaries of the workspaces of p lanar manipulators is presented. The numerical method consists of finding a suitable radiating point in the output coordinate space and then determini ng the points of intersection of a representative pencil of rays, emanating from the radiating point, with the boundary of the accessible set. This is done by application of a novel constrained optimization approach that has the considerable advantage that it may easily be automated. The method is i llustrated by its application to two planar mechanisms, namely a planar Ste wart terior boundaries of the workspace, interior curves that represent con figurations at which controllability and mobility may be limited, are also mapped. The optimization methodology, implemented here for the planar case, may readily be extended to spatial Stewart platforms.