Complete Shaking Force and Shaking Moment Balancing of Link Mechanisms Using Balancing Idler Loops

Abstract

A method for completely balancing the shaking forces and shaking moments in mechanisms is presented. The method introduces shaking moment balancing idler parallelogram loop (or loops) which transfers the motion of a coupler link to a shaft on the frame of the mechanism, where the rotary balancers balance the shaking moment. The complete balancing of a mechanism is accomplished by maintaining the total center of mass of the mechanism stationary meanwhile achieving that the total angular momentum of the moving links of the mechanism vanishes. Positioning of the idler loops is illustrated for a series of multiloop mechanisms. Theorems on the complete balancing of shaking forces and shaking moments in mechanisms are established. Design equations for completely balancing some single and multiloop mechanisms are given. A numerical example is included.