The chord method for the determination of nonconvex workspaces of planar parallel manipulators

An extension of a novel optimization approach for the determination of accessible output sets of planar manipulators is presented. The optimization approach provides a general method for the determination of workspaces and has the advantage that it allows for the easy and systematic implementation of constraints acting on manipulators. The previously proposed optimization methodologies, the ray method and modified ray method, were unable to map the boundaries of non-convex planar workspaces automatically. A new chord method is proposed in this paper, which allows for the automated and efficient mapping of most non-convex workspaces. The chord method is illustrated by application to three degree of freedom planar parallel manipulators of varied geometry. Indications are that further development of the algorithm will lead to a method that allows for the completely automated determination of planar manipulator workspaces.