Synthesis of Coupler Curves of Nongrashof Planar Four-Link Mechanisms by a Pattern Matching Method

• Published in: Transactions of the Japan Society of Mechanical Engineers Series C Vol. 67; no. 658; pp. 1965 - 1972
• Main Authors: Ying, Xu, WATANABE, Katsumi, KATOH, Hiroaki
• Format: Journal Article
• Language: Japanese
• Published: The Japan Society of Mechanical Engineers 2001
• Subjects: Arranging of Equi-distance Points; Coupler Curve; Four-Bar Linkage; Nongrashof Mechanism; Pattern Matching; Synthesis
• ISSN: 0387-5024; 1884-8354
• DOI: 10.1299/kikaic.67.1965

Nongrashof planar four-link mechanisms, that none of two neighboring links can make a complete rotation, generate complex coupler curves with highly nonuniform velocity when the driving link oscillates in such a manner that coupler and driven links belong to different composition loops in going and returning respectively. In this paper, for the purpose of classification and synthesis of nongrashof mechanisms, a procedure is presented for arranging points on the coupler curve with an equal distance, in which the input and output angles are interchanged according to whether the differential coefficient of the output angle is greater than some reference values or not. Furthermore, a pattern matching method is presented for synthesizing the coupler curve of the nongrashof mechanism. The method consists of magnification or reduction of the coupler curves, arrangement of equidistant points on desired and coupler curves, such a correspondence of points on both curves that the norm of the sampled values of their natural equations may be minimized and coordinate transformation of the coupler curve so that the maximum difference between both curves may be minimized.