No abstract

The increasing use of parallel cable-driven mechanisms calls for a better understanding of their behavior and highly efficient algorithms to attenuate their drawbacks at the design stage. One of these drawbacks is the high probability of mechanical interferences between the moving parts of the mechanism. In this paper, the phenomenon is described under the assumption that a cable is a line segment in space. When a mechanical contact occurs between two cables or between a cable and an edge of the end effector, these entities necessarily lie in the same plane, and then the three-dimensional problem becomes two-dimensional. This fact is used to simplify the equations, and leads to exhaustive descriptions of the associated interference loci in the constant-orientation workspace of a cable-driven mechanism. These results provide a fast method to graphically represent all interference regions in the manipulator workspace, given its geometry and the orientation of its end effector.

No abstract

An index is introduced, the minimum degree of constraint satisfaction, which quantifies the robustness of the equilibrium of an object with a single scalar. This index is defined under the assumptions that the object is supported by forces of known lines of action and bounded amplitudes, and that the external perturbation forces and moments vary within a known set of possibilities. A method is proposed to compute the minimum degree of constraint satisfaction by resorting to the quickhull algorithm. The method is then applied to two examples chosen for their simplicity and diversity, as evidence of the broad spectrum of applications that can benefit from the index. The first example tackles the issue of fastening a workpiece, and the second, the workspace of a cable-driven parallel robot. From these numerical experiments, the minimum degree of constraint satisfaction proves useful in grasping, cable-driven parallel robots, Gough-Stewart platforms and other applications.