Foundations for analytical models of staircase traversal of convex polygonal surfaces

In this paper, we present the analytical foundations for modelling the staircase traversal of convex polygonal surfaces by a tool in the form of a circular disk. Based on these foundations, we next develop a mathematical model and an algorithm for a near optimal tool path in a staircase traversal of convex polygonal surfaces. We compare this algorithm - which is called OPTPATH - with two existing algorithms. This comparison confirms that OPTPATH performs better than the other two test algorithms. The OPTPATH algorithm can be used for staircase traversal with or without overlap between successive sweep passes and with or without rapid traversal in edge passes. This generality of OPTPATH allows its application to several manufacturing problems such as face and pocket milling, robotic deburring, rapid prototyping, and robotic spray painting. The results of the theorems presented in the paper can be helpful in designing new algorithms as well as in improving some of the existing algorithms for optimizing tool path in staircase traversal of convex polygonal surfaces.