Simultaneous Optimization of Dynamic Reactions of a Four-Bar Linkage With Prescribed Maximum Shaking Force

Abstract

A three-counterweight technique for simultaneously minimizing the maximum values of such dynamic reactions as the bearing force, the input moment, and the shaking moment of a constant input speed four-bar linkage, while additionally obtaining a prescribed maximum value of the shaking force, is introduced. The chosen optimization formulation is new to the field of mechanism design; a certain minimization parameter is made the objective function. The maximum values of the individual dynamic reactions are then minimized by inequality constraints which force the differences between these reactions (due to the presence of counterweights) and the maximum value of the same reactions in the unbalanced mechanism to be smaller than the minimization parameter at as many mechanism positions as required. The prescribed maximum shaking force is attained by an equality constraint which has been called the general equipollent circle constraint equation. The method, which employs an augmented Lagrangian penalty function code, produced good results in the optimization of the dynamic reactions of partially and fully force balanced example mechanisms.