Kinematic Registration in 3D Using the 2D Reuleaux Method

This paper presents a method for kinematic registration in three dimensions using a classical technique from two-dimensional kinematics, namely the Reuleaux method. In three dimensions the kinematic registration problem involves reconstruction of a spatial displacement from data on a minimum of three homologous points at two finitely separated positions of a rigid body. When more than the minimum number of homologous points are specified or when errors in specification of these points are considered, the problem becomes an over determined approximation problem. A computational geometric method is presented, resulting in a linear solution of the over determined system. The results have applications in robotics, manufacturing, and biomedical imaging. The paper considers the kinematic registration when minimal, over-determined, infinitesimal, and perturbed sets of homologous point data are given.

Enumeration of Contact Geometries for Kinematic Registration Using Tactile Sensing Fixtures

This paper uses group theory for enumeration of contacts between geometric elements necessary for kinematic registration or part referencing in robotics. The results are applied to type synthesis of tactile sensing mechanical fixtures. Kinematic registration is an important step in robot calibration and in data driven automation. 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 calibration and part referencing.

Kinematic Registration Using Line Geometry

This paper uses line geometry to find an elegant solution to the kinematic registration problem involving reconstruction of a spatial displacement from data on three homologous points at two finitely separated positions of a rigid body. The bisecting linear line complex of two position theory in kinematics is used in combination with recent results from computational line geometry to present an elegant computational geometric method for the solution of this old problem. The results have applications in robotics, manufacturing, and biomedical imaging. The paper considers when minimal, over-determined, and perturbed sets of point data are given.