Synthesis of function generator four-bar linkages: Minimization of the joint-forces constraining structural-related quantities

Abstract

In the design process of a mechanism, the dynamic behavior plays an important role. It could be the cause of unexpected high dynamic forces in later stages when it is not considered in the early stage of the design process. High forces could produce high stresses and high vibration levels. Several studies have been carried out in this area; however, only a few consider structural criteria and the eigenfrequencies in the early stage of the process. Low forces and an adequate structure should lead to good dynamic behavior. In this work, we present a method to synthesize function generator four-bar linkages that takes into account structural criteria in a joint-forces minimization-maximization problem. Its objective function is the reaction force on the mechanism joints. The problem’s constraints are the maximum stress on the links, the first eigenfrequency of the mechanism and the deflection of the crank and the rocker. With this method, the links’ lengths and cross-sectional areas of the mechanism are obtained for a given task. As condition, we assumed that the crank rotates with constant angular speed and its shaft works as a torsional spring. Moreover, the rocker moves a body with constant inertia. The resultant mechanisms are compared with those obtained with a traditional crank-rocker synthesis method, according to VDI 2130. To compare both methods, the maximum force, maximum stress, deviation of the rocker angle at its dead-center positions and RMS vibration of the crank and rocker of each mechanism are calculated using MSC ADAMS™. The results show that the mechanisms obtained with our method have better stress and vibratory levels than those obtained with a traditional approach.