Synthesis Theory and Optimum Design of Four-bar Linkage with Given Angle Parameters

Abstract

Abstract. In this paper, a synthesis method is proposed for the 5-point-contact four-bar linkage that approximates a straight line with given angle parameters. The given parameters were the angles and the location of the Ball point. Synthesis equations were derived for a general Ball–Burmester point case, the Ball–Burmester point at an inflection pole, and the Ball point that coincided with two Burmester points, resulting in three respective groups of bar linkages. Next, taking Ball–Burmester point as the coupler point, two out of the three bar-linkage combinations were used to generate three four-bar mechanisms that shared the same portion of a rectilinear trajectory. Computation examples were presented, and nine cognate straight-line mechanisms were obtained based on the Roberts-Chebyshev theory. Considering that the given parameters were angles which was arbitrarily chosen, with the other two serving as the horizontal and vertical axes, so the solution region graphs of the solutions for three mechanism configurations were plotted. Based on these graphs, the distribution of the mechanism attributes was obtained with high efficiency. By imposing constraints, the optimum mechanism solution was straightforwardly identified by the designers. For the angular parameters prescribed in this paper, the solutions for three straight-line mechanism configurations were obtained, along with nine cognate straight-line mechanisms that shared the same portion of the rectilinear trajectory. All the fixed pivot installation locations and motion performances differed, thus providing multiple solutions to the trajectory of the synthesis of mechanisms.