Abstract
One of the most popular mathematical tools in the fields of robotics and mechanisms is the Denavit-Hartenberg (DH) notation (Denavit and Hartenberg, 1955, J. Appl. Mech., 77, pp. 215–221). It is valid only for mechanisms containing prismatic, revolute, helical, and cylindrical pairs, but cannot be applied to spherical pairs. This paper presents an extended DH notation that includes spherical pairs, consequently allowing the required independent parameters of any spatial binary mechanism to be listed for purposes of analysis and synthesis. Further, the interference-free region with maximum ball-retention capability of a socket in a spherical pair can be determined analytically. Extended DH notation can systematically model arbitrary binary mechanisms with spherical pairs, simplifying their design and study.
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