Research on Kinematics Based on Dual Quaternion for Five-axis Milling Machine

Abstract

This paper presents machine kinematics for five-axis milling machine, which uses a dual quaternion formulation of the kinematics equations. The goal of the machine kinematics is to evaluate a correct position of the parts in the workpiece. The workpiece of a constrained five-axis milling machine is a subset of the group of spatial transformations, in turn, which can be represented by a subset of dual quaternions. The basic approach is to specify the dual quaternion machine kinematics for each transformation of a discrete approximation to the desired workpiece. The structure of these dual quaternions has several advantages over the methods of Euler angles and rotation matrix. Here we present the theory and formulate the machine kinematics equations for a typical configuration of a five-axis milling machine. An application example is also presented.