Static balancing of 3-DOF planar parallel mechanisms

In mechatronic systems, the power transmission between the actuators and the mechanical elements is governed by the dynamic equations of the global system. One way of reducing the fluctuations of the required actuator forces or torques is to mechanically compensate for the gravity terms, a procedure which is referred to as static balancing. The static balancing of planar three-degree-of-freedom parallel mechanisms 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. For the mechanisms studied here, conditions for static balancing are obtained, and it is shown that balancing is generally possible, even when the dimensional parameters are imposed, which is a useful property since dimensional parameters are usually obtained from kinematic design or optimization. Then, the conditions for the static balancing of the same mechanisms are derived for designs in which elastic elements are included, Finally, examples of balanced mechanisms are given. A dynamic study is performed, and it is shown that the positioning of the counterweights can affect the inertia of the system and that the elastic elements can be used to minimize this inertia. 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 for mechatronic systems.