Static balancing of spherical 3-DoF parallel mechanisms and manipulators

The static balancing of spherical three-degree-of-freedom (DoF) parallel mechanisms and manipulators is addressed in this paper Static balancing is defined here as the set of conditions on mechanism dimensional and inertial parameters which, when satisfied ensure that the weight of the links does not produce any torque (or force) at the actuators for any configuration of the mechanism, under static conditions. First, the static balancing of a single body mounted on a spherical joint is studied. It is shown that it is possible to balance such a mechanism with springs, and that complete balancing can be achieved even with a single spring. Geometric conditions for the location of the spring attachments are given. Then, the results are applied to the balancing of two types of 3-DoF spherical parallel mechanisms. The first mechanism is a 9R manipulator while the second one is referred to as the 3-6-6 spherical mechanism. For each of these mechanisms, the balancing conditions 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 more efficient designs. Hence, the balancing conditions derived here are of great interest in a context of design.