THE DEGENERATED SPHERICAL BURMESTER CURVES OF THE PP-P-P CASE

In this paper an analytic method to investigate the degenerated spherical Burmester curves of the PP-P-P case is presented. (Provided that an instant centre and two poles associated with two rotation angles of a coupler are specified, a geometric construction is established to determine the spherical centre- and circle-point.) According to the geometric construction, the explicit equations of spherical Burmester curves for the PP-P-P case are thus derived, without the use of differentiation, but by using spherical cross ratio. By assigning proper parameter values to equations obtained, six types of degenerated spherical Burmester curves of the PP-P-P case are obtained directly, which include three different forms of the degenerated curve: (1) a point, (2) a great circle and a spherical Thales ellipse and (3) three great circles.