Abstract

This brief, approximately chronological, paper is about two special types of linkages for converting rotational or oscillatory input motion into an approximate linear or circular motion. Decades long development of the concepts of Inflection Circle and Circling Point curves (Cubic of Stationary Curvature) for anticipating an approximate straight line or an approximate circular arc in the coupler curve is described with minimal inclusion of the mathematical expressions and significant steps essential for their development. This paper presents the much-required rich background to have a relook at the almost forgotten achievements of matured topics like differential geometry, kinematic geometry, and kinematics of mechanisms with graphical approaches. Historically the Path Curvature theory had arrived at the methodology to anticipate the best possible coupler geometry to trace the longest approximate straight line path for the selected pose of the input link of the planar linkage. This paper revisits the long history of almost eighteen decades (1700–1880) to enrich the present-day data sets, with limiting values, to be used for data driven synthesis. After rekindling of interest in these topics, interdisciplinary researchers can select and use any one of present day digital, i.e. Machine Learning, techniques to overcome the hurdles faced by the experts of yesteryears.