Introducing Radius of Torsure and Cylindroid of Torsure

Abstract

Abstract Robotic path planning can involve the specification of the position and orientation of an end‐effector to achieve a desired task (e.g., deburring, welding, or surface metrology). Under such scenarios the end‐effector is instantaneously rotating and translating about a unique axis; the ISA. Alternately, the performance of direct contact mechanisms (viz., cam systems and gear pairs) are dependent on the surface geometry between two surfaces in direct contact. Determination of this geometry can entail the parametrization of a family of geodesics curves embedded within each surface. This parametrization is tantamount to an end‐effector rotating and translating about an ISA. In both scenarios there is a unique ISA for each geodesic embedded in a surface. Here, curvature and torsion of a spatial curve are coupled together to define an alternative definition for the radius‐of‐curvature of a spatial curve. This new definition is identified as radius of torsure to distinguish it from the classical definition for radius‐of‐curvature. Further, it is shown that the family of twists that corresponds to the pencil of geodesics coincident with a point on a surface defines a cylindroid: the cylindroid of torsure. An illustrative example is provided to demonstrate this difference. © 2003 Wiley Periodicals, Inc.