Complete Shaking Force and Shaking Moment Balancing of Mechanisms Using a Moving Rigid Body

Abstract

This paper addresses the mass balancing of mechanisms using a single rigid body („balancing body“). Firstly, the expressions of dynamic forces and moments acting on the machine frame, which are caused by arbitrary planar and spatial mechanisms are established. The general balancing conditions are then derived. By motion control of the balancing body, any resultant inertia forces and moments of several mechanisms can also be fully compensated. The desired motion of the balancing body is calculated in order that the sum of inertia forces and moments of the mechanisms and the balancing body is zero. Theoretically, the balancing body is possible to compensate the dynamic loads of the machine frame, even if several mechanisms with any structure are located in the machine frame. The balancing theory of planar mechanisms is presented in more detail. Finally, the proposed balancing method is illustrated by a numerical example, in which three components of dynamic loads caused by a planar mechanism in the steady state are given as the time-periodic functions. It can be shown that the proposed approach is an alternative to the conventional balancing methods and especially applicable in practice with piezoelectric actuators.