A Statically Balanced Gough/Stewart-Type Platform

Gravity compensation of spatial parallel manipulators is a relatively recent topic of investigation. Perfect balancing, by either counterweights or elastic elements, has been accomplished, so far, only for parallel mechanisms in which the weight of the moving platform is sustained by legs comprising purely rotational joints. Indeed, balancing of parallel mechanisms with translational actuators, which are among the most common and used ones, has been traditionally thought possible only by resorting to additional legs containing no prismatic joints between the base and the end-effector. This paper presents the conceptual and mechanical design of a balanced Gough/Stewart-type manipulator, in which the weight of the platform is entirely sustained by the legs comprising the extensible jacks. By the integrated action of both elastic elements and counterweights, each leg is statically balanced and it generates, at its tip, a constant force balancing the weight of the end-effector in any admissible configuration. If no elastic elements are used, the resulting manipulator is balanced with respect to the shaking force too. Two Appendices are also provided, presenting formal and novel derivations of the necessary and sufficient conditions allowing i) a body arbitrarily rotating in space to rest in a state of neutral equilibrium under the action of general constant-force generators, ii) a body pivoting about a universal joint and acted upon by a number of zero-free-length springs to exhibit constant potential energy regardless of its configuration.