Finite position method for complete balancing of shaking forces of mechanisms

Finite positions method is presented in this paper for complete balancing of shaking forces for planar and spatial mechanisms as well as the solutions to its equations. By using the method, only correctly formulated single-linked-chains (SOC) with proper connection and leaf components are needed to substitute into the equations to solve the parameters, which will be used to fully balance the shaking forces of planar mechanisms. The equations can be generated automatically. Furthermore, the equations are so flexible that they can solve the equilibrium of spatial mechanisms. This method can be applied to any complex planar or spatial mechanisms upon completion of positional analysis. It is easier than linearly independent vector method and has wider range of applications. In the end, the detailed steps of the method are given for solving planar single loop four-bar (RRRR and RRRT), planar double loop six-bar (RRRRRT), and spatial single loop (RSCR) mechanisms.