Abstract
This paper uses group theory for enumeration of contacts between geometric elements necessary for part registration and referencing in robotics. The results applied to type synthesis and design of tactile sensing mechanical fixtures. Although the scope of the paper is limited to geometric contacts involving points, lines, planar surfaces, cylindrical surfaces, and spherical surfaces, the techniques developed are general and can be applied to other geometric features and non-tactile sensing elements used in robotic calibrations and part referencing.