New interval-based approach to determine the guaranteed singularity-free workspace of parallel robots

In the present paper we introduce an improved method to obtain the guaranteed singularity-free workspace of planar parallel kinematic machines. A geometric condition for the existence of singularities is extended to be used in interval analysis. Therefore, we eliminate the need of calculating the inconvenient interval form of the Jacobian´s determinant. Hence, an appropriate description of the singularity-free workspace is obtained and the computational effort is reduced significantly. With the interval-based approach error sources, like manufacturing tolerances, can be considered. Consequently, regions that do not satisfy the proposed condition can be guaranteed not to have any type-two singularities. Several analysis examples demonstrate the efficiency of the proposed geometrical-based solver in comparison to existing solvers, i.e. based on the Jacobian´s determinant.