Determination of shortest distances in the three dimensional task space of robots is pertinent to pick-and-place operations, collision avoidance, and for impact prediction in dynamic simulation. The conventional approach is to find perpendicular distances between planar patches approximating body surfaces. In contrast, this paper treats four variants of shortest distance computations wherein one or both elements are circular edges. These three dimensional cases include circle and point, circle and plane, circle and line and two non coplanar circles. Solutions to these four fundamental problems are developed with elementary geometry. Examples are presented, and the closed form algebraic solutions are verified with descriptive geometric constructions.

Additional Metadata
Journal Transactions of the Canadian Society for Mechanical Engineering
Citation
Zsombor-Murray, P.J. (P. J.), Hayes, M.J.D, & Husty, M.L. (M. L.). (2004). Extreme distance to a spatial circle. In Transactions of the Canadian Society for Mechanical Engineering (Vol. 28, pp. 221–235).