On the Existence of Circle-Point and Center-Point Circles for Three-Precision-Point-Dyad Synthesis

Abstract

A graphical method is developed for expressing solutions to all possible revolute dyad, three finitely separated position synthesis problems, where any two rotational displacements are prescribed. Also, cases are discussed where two positions and one velocity are prescribed. The three-precision-point solutions are shown to be represented by circular loci of fixed and moving dyad pivots that are derived from an analytical treatment based on bilinear transformation of the synthesis equations. The superposition of two three-position dyad problems with two common positions yields points on the four-precision-point Burmester curves satisfying both problems. A new alternative explanation for the classical Burmester curve construction is offered. Regions of the plane are found where dyad moving pivots cannot exist for a given problem. Computer graphics output is used to demonstrate several typical solutions.