The algorithm developed in  for searching for extreme distance lines of robot arms with arbitrary skew joint axes can fail when applied to arms with special geometry. In this paper, procedures are developed to search for extreme distance lines of robot arms with intersecting or parallel axes. Such cases have important practical application. It is demonstrated that a robot arm with geometry common to industrial arms such as Cincinnati Milacron, Hitachi (Japan), Trallfa (Norway), Puma (Unimation), ASEA (Sweden), Volkswagen and Kuka (Germany) has a total of sixty-four extreme distances.
Determination of Extreme Distances of a Robot Hand. Part 2: Robot Arms With Special Geometry
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Sugimoto, K., and Duffy, J. (October 1, 1981). "Determination of Extreme Distances of a Robot Hand. Part 2: Robot Arms With Special Geometry." ASME. J. Mech. Des. October 1981; 103(4): 776–783. https://doi.org/10.1115/1.3254987
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