Static balancing of spherical 3-DoF parallel mechanisms and manipulators

The static balancing of spherical three-degree-of-freedom (DoF) parallel me chanisms and manipulators is addressed in this paper Static balancing is de fined here as the set of conditions on mechanism dimensional and inertial p arameters which, when satisfied ensure that the weight of the links does no t produce any torque (or force) at the actuators for any configuration of t he mechanism, under static conditions. First, the static balancing of a sin gle body mounted on a spherical joint is studied. It is shown that it is po ssible to balance such a mechanism with springs, and that complete balancin g can be achieved even with a single spring. Geometric conditions for the l ocation of the spring attachments are given. Then, the results are applied to the balancing of two types of 3-DoF spherical parallel mechanisms. The f irst mechanism is a 9R manipulator while the second one is referred to as t he 3-6-6 spherical mechanism. For each of these mechanisms, the balancing c onditions are first derived for systems in which no springs are used. Then, conditions for the balancing using springs are obtained. Static balancing leads to considerable reduction in the actuator torques (or forces), which in turn allows the use of less powerful actuators and therefore leads to mo re efficient designs. Hence, the balancing conditions derived here are of g reat interest in a context of design.