4. Complete Shaking Force and Shaking Moment Balancing of Linkages

In this Chapter, new methods for the full shaking force and shaking moment balancing of linkages are considered. In Sect. 4.1, a new solution for the full shaking force and shaking moment balancing of four-bar linkages is discussed, which allows the complete shaking force and shaking moment balancing of in-line four-bar linkages with constant input speed by adding a class-two Assur group, i.e. a group which does not add any supplementary degree of freedom into the mechanism. It should be noted that the balancing of the shaking moment without counter-rotations of three particular classes of four-bar linkages is known and it was mentioned in the overview (see Sect. 2.1). However, such a method cannot be extended to general four-bar linkages. In the mentioned Section, it is proposed to dynamically balance the in-line four-bar linkages by adding articulated dyads.

The object of the approach presented in Sect. 4.2 is to provide the conditions for a complete shaking force and shaking moment balancing of linkages with a relatively small increase of the total mass of movable links by mounting the gear inertia counterweights on the base of the mechanism. The method involves connecting to the mechanism to be balanced a two-link group forming a pantograph with the crank and coupler. Three versions of sub-linkages are considered: (1) the articulation dyad; (2) the asymmetric link with three rotational pairs; (3) the crank-slider mechanism. The method is illustrated by new balancing schemes for the Stephenson and Watt linkages. An advantage of the schemes outlined here is the fact that all the gear inertia counterweights needed for balancing the shaking moment are mounted on the mechanism frame, which is constructively more efficient.