Machine models and tool motions for simulating five-axis machining

This paper presents a method of determining the tool motion of a five-axis machine. The method is motivated by the imprint point method, where points on the machined surface are computed based on the tool position and tool motion. While simple linear motion can be used as a coarse approximation to this motion, this paper looks at more accurate models of tool motion based on machine kinematics that can be generalized and applied to any CNC machine with one tool head. A kinematic chain is created by decomposing the linear motion of a machine's translational and rotational axes into parameterized affine transformations, and a hierarchical model of the machine combines the transformations to provide an accurate model of machine motion.