Determining Burmester Points from the Analysis of a Planar Platform

This paper presents a technique for determining the Burmester points of five finitely separated positions in a plane. A Burmester point is the location of the fixed pivot of an RR dyad that can reach each of the five positions. These Burmester points are obtained from a compatibility platform constructed from selected relative poles associated with the five specified displacements. We show that the relative position pole of two assembly configurations of this platform is a fixed pivot compatible with the five positions. An example originally presented by Sandor and Erdman is used to verify the calculations.