CENTER-POINT CURVES THROUGH 6 ARBITRARY POINTS

A circular cubic curve called a center-point curve is central to kinem atic synthesis of a planar 4R linkage that moves a rigid body through four specified planar positions. In this paper we show the set of circ le-point curves is a non-linear subset of the set of circular cubics. In general, seven arbitrary points define a circular cubic curve; in c ontrast, we find that a center-point curve is defined by six arbitrary points. Furthermore, as many as three different center-point curves m ay pass through these sir points. Having defined the curve without ide ntifying any positions, we then show how to determine sets of four pos itions that generate the given center-point curve.