Burmester lines of spatial five position synthesis from the analysis of a 3-CPC platform

This paper presents a new technique for determining the fixed axis for a sp atial CC chain that guides a rigid body through five finitely separated pos itions, termed a Burmester Line. It is known that there can be as many as s ix Burmester lines for a given set of five spatial positions. Here we show that these six lines can be obtained from the analysis of a 3-CPC platform, constructed from relative screw axes associated with the five specified di splacements. The screw axes of the displacement of this platform to each of its assemblies are the desired Burmester lines. Roth's original example is presented to verify the calculations.