ON EXPLICIT EQUATIONS OF THE BURMESTER CURVES FOR THE PPP-P CASE IN SPHERICAL MOTION

In this paper, an analytic treatment to investigate the Burmester curv es of the PPP-P case in spherical motion is presented. With a rotation angle of a coupler about a pole and an instant centre associated with an inflection point specified, a geometric construction is establishe d to deter mine the corresponding spherical centre-points and circle-p oints. According to the geometric construction, the explicit equations of spherical Burmester curves for the PPP-P case are directly derived by using spherical trigonometry, without the use of differential tech nique. The explicit equations obtained give a clear insight into the g eometric properties and special cases of the spherical Burmester curve s, which include degenerated curves and symmetric curves. A design app lication is presented. (C) 1998 Published by The Franklin Institute. P ublished by Elsevier Science Ltd.