Robot Workspace of a Tool Plane: Part 1—A Ruled Surface and Other Geometry

Abstract

The sweeping process is used for conceptually describing plane-workspaces and for distinguishing certain forms of these workspaces for robots. The tangent point to the plane-workspace of a tool plane σ is identified as the intersection point of σ with that extreme-distance line which is also normal to σ. The quartic ruled surface, which is a new property of the dual torus, is identified and described. It contains information that uniquely identifies the 2-R manipulator which generates the dual torus. these geometric features are then used in developing the equations for computer generation of plane-workspace envelopes and boundaries for an n-R robot.