Abstract
In this study, new geometrical constructions and simplified equations are proposed to determine the center- and circle-point curves of four-bar linkages with specified first derivative of motion. Properties and degenerations of the curves can easily be investigated by the proposed methods. By using the degenerate curves, the equations for evaluating the Burmester centers are greatly simplified to cubic and quadratic equations. The methods proposed herein can be applied directly to the synthesis of linkages for motion generator, path generator, and function generator with specified first derivative of motion. Interesting applications are presented for illustrating the entire techniques.
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