In this paper, a synthesis method is proposed for the5-point-contact four-bar linkage that approximates a straight line withgiven angle parameters. The given parameters were the angles and thelocation of the Ball point. Synthesis equations were derived for a generalBall–Burmester point case, the Ball–Burmester point at an inflection pole,and the Ball point that coincided with two Burmester points, resulting inthree respective groups of bar linkages. Next, taking Ball–Burmester pointas the coupler point, two out of the three bar-linkage combinations wereused to generate three four-bar mechanisms that shared the same portion of arectilinear trajectory. Computation examples were presented, and ninecognate straight-line mechanisms were obtained based on theRoberts-Chebyshev theory. Considering that the given parameters were angleswhich was arbitrarily chosen, with the other two serving as the horizontaland vertical axes, so the solution region graphs of the solutions for threemechanism configurations were plotted. Based on these graphs, thedistribution of the mechanism attributes was obtained with high efficiency.By imposing constraints, the optimum mechanism solution wasstraightforwardly identified by the designers. For the angular parametersprescribed in this paper, the solutions for three straight-line mechanismconfigurations were obtained, along with nine cognate straight-linemechanisms that shared the same portion of the rectilinear trajectory. Allthe fixed pivot installation locations and motion performances differed,thus providing multiple solutions to the trajectory of the synthesis ofmechanisms.
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