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.

This paper presents ARACHNIS, a graphical user interface for the analysis and parametric design of Cable Driven Parallel Robots (CDPRs). ARACHNIS takes as inputs the design parameters of the robot, the task specifications, and returns a visualisation of the CDPR Wrench Feasible Workspace (WFW) and Interference-Free Constant Orientation Workspace (IFCOW). The WFW is traced from the capacity margin, a measure of the robustness of the equilibrium of the robot. Interferences between the moving parts of a CDPR are also determined by an existing technique for tracing the interference-free workspace of such robots. Finally, the WFW and the IFCOW of a planar cable-driven parallel robot and of a spatial cable-driven parallel robot are plotted in order to demonstrate the potential of ARACHNIS.

Abstract. This paper presents recent advances in the design of an underactuated hand for applications in prosthetics. First, the design of the fingers is addressed. Based on previous experiments with prototypes developed in the past, new tendon routings are proposed that lead to a more effective transmission of the forces. A novel elastic tendon routing is also proposed for the passive opening of the hand. A simplified static analysis of the fingers is proposed to support the results. Then, a new kinematic design of the thumb is presented. The thumb is designed to perform out-of-the-plane motions in order to broaden the variety of possible grasps. A mechanism for the implementation of underactuation between the fingers is proposed that alleviates the friction problems encountered in earlier hand designs. Finally, a prototype of the hand is briefly described and typical grasps are shown.

Considering the many advantages of underactuation in anthropomorphic hands, such as lightness, ease of control and compactness, it is of interest to develop mechanisms that aim at achieving underactuation between the fingers. This paper presents several tendon-driven underactuated mechanisms that can drive four outputs from one input. These mechanisms could typically be used to drive four fingers of an underactuated hand from a single input. Among these mechanisms, some are built by combining one-input/two-output differential mechanisms, while others are fully integrated systems of pulleys. For each mechanism, a static analysis is presented. Then, a discussion based on the static analysis and experimentation on models highlights their strengths and weaknesses. Finally a new anthropomorphic hand used as an experimental platform to test these mechanisms is introduced.

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