Abstract
A robot arm is in effect a smooth function from the space of positions of the arm to the space of positions of a coordinate frame attached to the end of the arm. For the most common robots built today, this means a map f: T n→R 3×SO 3. We describe the singularities of this map. The set of rotational singularities is the set of arm positions where the axes of the links are parallel to a plane. Thus, it is always two-dimensional. Also, we show that f is homotopic to a map which factors through a circle, and represents the generator of π1(SO 3). The engineering implication of these statements are discussed.
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Gottlieb, D.H. Topology and the robot arm. Acta Appl Math 11, 117–121 (1988). https://doi.org/10.1007/BF00047283
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DOI: https://doi.org/10.1007/BF00047283