Sculpturing surfaces with robot manipulators

© 1993 Dr. Colin Reginald BurvillA six freedom robot manipulator can position and orientate a tool anywhere within in its workspace. This enables the manipulator to traverse an oriented cutting tool across surfaces whose topography require the use of all six freedoms. Although the tracing of a general curve within the reachable workspace is theoretically possible, kinematic and control limitations often preclude this. The degree of such limitations may impede the successful generation of a specific surface shape. This research investigated specific surfaces and sculpturing strategies to evaluate the kinematic limitations posed by manipulators. In the assessment of whether a strategy will be successful or not, the manipulator's structural configuration, cutting tool geometry, location of the surface in the workspace, and the trajectory generation method must be taken into consideration. The range of end-effector orientations possible at a single position within the manipulator's workspace was defined as the orientation envelope and provides a measure of manipulator dexterity. The orientation envelope can be used to predict whether a manipulator based sculpturing system can kinematically complete a sculpturing strategy. Surfaces that cannot be sculptured continuously, either due to orientation envelope or dexterity limitations, may be divided into patches, each involving a different strategy. At a special configuration the rank of a six freedom manipulator's Jacobian is less than six because at least two joints lose their linear independence. Special configurations are likely to be encountered during sculpturing of highly curved surface regions and can prevent continuous sculpturing. To permit continuous sculpturing in a. region which contains special configurations, the trajectory curves for the manipulator are either steered away from singular positions on the surface or made to move smoothly through them by adjusting the trajectory path. A system based interface between the Cincinnati Milacron T3-726 controller and an external host computer was written to test the accuracy of the T3-726 in locating end- effector geometries in its workspace during tracing experiments. The T3-726 controller introduced a substantial systematic error which caused end-effector locational errors that tended to increase as the manipulator actuated its joints away from their home positions. Manipulator based sculpturing can only be performed reliably with external joint space control. A novel method of trajectory curve generation is proposed in which only a surface and an initial surface curve description is needed. The evolution of the initial surface curve is driven by the curvature of the curve and the surface to which it is constrained and subsequently generates a family of intermediate trajectory curves