A simple matrix method for the force balancing of planar multi-degree-of-freedom linkages

The shaking or fluctuating reaction forces produced by the moving links of a mechanism negatively impact its adequate performance due to the inherent generation of base vibrations, fatigue stresses, accuracy loss of the end-effector or moving platform, and so on. To increase the functionality and durability of the mechanism is therefore strongly advised to eliminate these parasitic forces. This article provides the balancing conditions for planar multi-degree-of-freedom linkages by canceling the total shaking force generated by the moving links of the mechanism. The method avoids the classical computation of the total linear momentum employed in existing methods. The balancing of three representative linkages proves the reliability of the proposed method.