Abstract
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.
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callMore From: Transactions of the Canadian Society for Mechanical Engineering
Disclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
