The paper is divided into three parts concerned with the Burmester points associated with five distinct positions of a plane. In the first part, “Theory,” an equation is derived for the location of the Burmester points; algebraic and geometric properties of these points are deduced and special cases considered. An automatic digital-computer program is described in the second part, “Computation,” using a parametric form of the equation for the Burmester points. In the third part, “Application,” the analytical form of Burmester theory is applied to the solution of a variety of problems in plane kinematic synthesis in one uniform manner.

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