Wrench capability in redundant planar parallel manipulators with net degree of constraint equal to four, five or six

This paper presents three mathematical closed-form solutions to obtain the maximum force with a prescribed moment in redundant planar parallel manipulators with a net degree of constraint equal to four, five or six. The proposed mathematical models are obtained integrating the screw theory, Davies method and classical optimization methods as primary mathematical tools. The greatest impact of the mathematical closed-form solutions proposed in this study lies in the fact that the force capability of manipulators with a net degree of constraint equal to four, five or six can be obtained in a direct way and without the use of a method or a numerical algorithm, representing an easier, faster, more direct and more versatile way to solve the force capability problem in manipulators satisfying the established net degree of constraint. The proposed mathematical closed-form solutions are general and can be applied to any redundant planar parallel manipulators with a net degree of constraint equal to four, five or six and they can be used in applications requiring a real-time response in terms of force capability. Some force capability polygons and polytopes are obtained for different manipulators in order to exemplify the use of the mathematical closed-form solutions.