Career
His doctoral thesis Über die Elemente einer Theorie der Isophoten (About the elements of a theory of isophotes) concerned lines on a surface defined by light direction. Burmester considered both the theory of planar kinematics and practically all actual mechanisms known in his time. In doing so, Burmester developed Burmester theory which applies projective geometry to the loci of points on planes moving in straight lines and in circles, where any motion may be understood in relation to four Burmester points.
The Burmester linkage of 1888 is a four bar linkage part of whose coupler curve is an approximately straight line (see also Watt"s linkage).
A French curve may also be known as a Burmester curve.