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Kinematic Analysis of Spherical Four-Bar Linkages via the Inflection Cubic and Thales Ellipse

[+] Author Affiliations
Giorgio Figliolini

University of Cassino & Southern Lazio, Cassino, FR, Italy

Jorge Angeles

McGill University, Montréal, QC, Canada

Paper No. DETC2015-47571, pp. V05CT08A046; 10 pages
  • ASME 2015 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference
  • Volume 5C: 39th Mechanisms and Robotics Conference
  • Boston, Massachusetts, USA, August 2–5, 2015
  • Conference Sponsors: Design Engineering Division, Computers and Information in Engineering Division
  • ISBN: 978-0-7918-5714-4
  • Copyright © 2015 by ASME


The subject of this paper is the formulation of a specific algorithm for the kinematic analysis of spherical four-bar linkages via the inflection spherical cubic and spherical Thales ellipse by devoting particular attention to the crossed four-bar linkage (anti-parallelogram).

Moreover, both the inflection and the elliptic cones, which represent the equivalent of the Bresse cylinders of the planar case in three-dimensions, are obtained by showing the particular properties of the spherical motion in terms of the curvature of a coupler curve and both the velocity and acceleration vector fields.

Of special interest are also the cases in which the three acceleration poles coincide at one unique point or in two plus one, which depends on the intersections of two spherical curves of third and second degree.

Copyright © 2015 by ASME



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