Determination of 5-axis tool orientation using analogy between parametric surface and form shaping function

Abstract

This paper describes a method to determine tool orientation in a 5-axis machine tool. In simultaneous 5-axis machining, the tool orientation must be determined uniquely from infinite options based on a strategy implemented with computer-aided manufacturing (CAM) software. In general, tool orientation is determined by constraining several conditions, such as avoiding singularities and collisions between the tool and the workpiece and creating a smooth tool trajectory. This paper proposes a new method using an analogy between a parametric surface and the form-shaping function of the target machine tool. This paradigm means that the constraint process of tool path generation can be converted to geometric problems on the surface comparable to the form-shaping function. For example, an intersection line between the surface and a plane provides a constraint that fixes specific axes on the machine tool. This method furthermore has good compatibility with the tool configuration space (C-space). That is, the parametric space composed of two parameters of the parametric surface is synonymous with the C-space. First, the proposed method is illustrated, and then two cases without collision avoidance and one case based on C-space are demonstrated.