Transmission angle of planar four-bar linkages applicable for different input-output links subject to external loads

The transmission angle is a traditional performance indicator in planar four-bar linkages, whereby force and motion are transmitted from the input link to the output link. However, for the calculation of traditional transmission angle, it is predefined that the input and output links are connected to the fixed link, i.e., the grounded link. This brings the problem of calculating the transmission angle for other cases, for example, the coupler link being the input link. Moreover, the traditional transmission angle cannot evaluate the influence of external loads on the transmission quality. In this work, we revisit this problem and redefine the transmission angle, which allows us to investigate the effect of different selections of the input and output links and external loads on the transmission performance. A case study of transmission angle analysis of a planar four-bar linkage is included to illustrate the application of the revised performance index. Moreover, three new transmission quality indices are introduced, upon which transmission performance optimization of a planar four-bar linkage is presented. Based on the redefined transmission angle and the proposed transmission quality indices, transmission quality analysis and optimal design of general four-bar linkages can be conducted to enhance their transmission performances.