Optimum balancing of a class of multiloop linkages by function cognate transformations

Abstract

The paper deals with the well-known class of complex mechanisms which remain kinematically invariant (function cognates) w.r.t. the angular rearrangement of their sub-linkages, and reveals the potentials of these transformations for optimum balancing of such mechanisms. Providing complete shaking force balancing, two general problems are specifically discussed: (a) minimization of the total balancing mass, and (b) shaking moment minimization. An essentially general analysis provides all basic results in explicit form, proves the existence of conjugate solutions correspondent to equal balancing masses, and establishes nontrivial situations when certain counterweights are completely canceled. A series of examples illustrate the theory, its merits and limitations.