Haptic displays are special devices, able to provide the sense of force or moment feedback to the human operator by rendering a variable mechanical impedance. They are widely used in Virtual Reality, teleoperation and virtual-drive systems. In this paper, the problem of measuring the force-exertion capability of a spatial cable-driven haptic display is addressed. A new set of manipulability indexes that applies to all completely restrained cable-based spatial systems is developed, by generalizing a set of indexes previously introduced for planar devices. These indexes can be used to analyze the working space of cable-based devices and/or to optimize their parameters (e.g., the locations of cable attachment points). In the paper, the set of manipulability indexes is applied to the analysis of a desktop cable-driven haptic display, called the PiRoGa5. PiRoGa5 is a 5 degree-of-freedom haptic pen, driven by 6 cables that are arranged to form two opposite pyramids, whose bases lay in two parallel planes and whose vertexes coincide with the ends of the pen-like end-effector. Wires are wound onto pulleys, pass through fixed eye-bolts, and are alternatively fixed to the upper and lower ends of the end-effector. The kinematics of the system is derived first, and position accuracy is inspected. Secondly, the new manipulability indexes are employed to determine and optimize the working space of the haptic device. Finally, a method is presented to analytically compute the wire tensions for a given wrench.

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