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This paper addresses determination of constraint wrenches in singularities. The constraint wrenches imposed to the mobile platform by kinematic chains is proposed approach to rely on the theory of screws and influences of the criteria of singularity analysis to corresponding results for design of the parallel mechanisms. Further, using of the screw groups in order to determination of the singular zones of the multi-DOFs parallel mechanisms that make form of continuous areas is considered. Beside, automation of designing a parallel mechanism, which in purpose to achieve an increase their working volume, dexterity, and stiffness is developed. The method is used to propose optimal design of the parallel mechanisms based on the multi-criteria optimization obtaining the Pareto-optimal.