Computational Issues in the Kinematic Design of Tactile Sensing Fixtures

This paper discusses computational issues in kinematic design of tactile sensing fixtures used in robotics applications. It deals with mechanical fixtures built or modeled by feature surfaces consisting of planes, spheres, and cylinders. It develops the governing equations for locating each of these geometric objects using tactile sensing probes. It shows that although four points are needed to locate a sphere, in many applications sensing three points is sufficient for referencing. In the case of a cylinder it is shown that in general six points are necessary and that in many applications five points are sufficient for locating the cylinder. The paper reduces the governing equations for a cylinder to a set of polynomial equations consisting of a second-degree and a third-degree equation. The solutions of this set are found using symbolic computations. The results are applied to the kinematic design and analysis of a mechanical fixture consisting of a sphere and a cylinder as its feature surfaces.