The Grand 4R Four-Bar Based Inherently Balanced Linkage Architecture for synthesis of shaking force balanced and gravity force balanced mechanisms

Considering balancing as starting point in the design of mechanisms and manipulators is known as inherent balancing. Inherently balanced linkage architectures then form the basis from which balanced mechanism solutions are synthesized, needing no countermasses contrary to balancing of given mechanisms. In this paper a new and advanced inherently balanced linkage architecture with the 4R four-bar linkage as a basis is presented, the Grand 4R Four-Bar Based Inherently Balanced Linkage Architecture. With 24 links it is 26 times overconstrained yet movable with stationary center of mass. It is shown that all theories for tracing the center of mass of a four-bar linkage are found inside. It is shown also how from this architecture a variety of new normally constrained 2-DoF balanced linkages are derived by removing a selection of links. This is done for the situations that all links are mass symmetric, for which 32 solutions are presented, and that all links have a general mass distribution. As an example, the balance conditions for the TWIN-4B, a solution of two similar 4R four-bar linkages, one inside the other, are derived and it is shown how this solution can be transformed into a spatial inherently balanced double Bennett linkage.