A New Version of Five-Axis Motion of Spheres with Spacelike Curves in Minkowski Space

In this paper, we investigate efficient parametric approach of determining the motion of the envelope surface by a spacelike curve in E³ ₁. In this new method the cutteris modeled as a canal surface. Also, cutter surfaces performing 5-axis tool motions are decomposed into a set of characteristic circles. For obtaining these circles a new method two-parameter-family of spheres is introduced. In this concept the center of a moving sphere is a function of two parameters representing the cutter surface and the tool motion. Using the Frenet frame of the given curve, we obtain new Drichlet approach for five-axis canal surface. Finally, we obtain minimality of five axis surfaces by using Drichlet approach.