Conditions of proper sculptured surface machining on polar coordinates

Multi-axis machining of sculptured surfaces is in wide use in conventional and rapid prototyping. Topic of the paper is in the area of sculptured surface machining on polar coordinates. The problem under consideration is: How to define and how to analytically describe a set of necessary and sufficient conditions of proper SSM. The similar problem is already solved with respect to machining of sculptured surface by Stephen P. Radzevich . Here this problem is enhanced up to the area of machining of sculptured surface on polar coordinates NC machine. The general approach to solve the problem is developed. The input data to the approach presented later is a complete information of topology of a sculptured surface to be machined on polar coordinates and of the machining surface of a form cutting tool to be applied. The set of six necessary and sufficient conditions of proper SSM is developed as a result. This set of analytically described conditions can be considered as a sort of restrictions on the geometrical and kinematical parameters of a machining operation. The methodology presented here is a general one. It combines the activities of exploration of topology of a given sculptured surface, of the machining surfaces of a form cutting tool, and of kinematics of relatives motion of these surfaces in machining operation, thus making the production process for conventional and rapid prototyping flexible, automatic and controllable.