Structural characteristics of force/moment polytopes of cable driven parallel mechanisms

Abstract

The force/moment capability of cable driven parallel mechanisms is characterized by force/moment polytopes resulting from a linear transformation between the space of cable tension and the space of the force/moment of the moving platform. Conventional method developed in computational geometry has been used to identify the vertices and faces of the polytopes. In this paper, we explored the relationship between the polytopes and the structure of a cable driven parallel mechanism and proposed a new method to identify the vertices and the faces of the polytopes. We analyzed the characteristics of the hyper cuboid defined by the minimum and maximum cable tensions and took into account inherent relationships between all vertices and faces of the polytopes. By utilizing the inherent relationships, we were able to show the relationships between the force/moment polytopes and the cable directions. These relationships are potentially useful for the design of cable driven parallel mechanisms. As an example, the polytopes of a 9-cable driven 6-DOF parallel mechanism are presented.