Modelling of Five-Axis Machine Tool Metrology Models Using the Matrix Summation Approach

Five-axis machining has been used widely in manufacturing freeform surfaces. The traditional approach of using a homogeneous transformation matrix (HTM) relies on heavy symbolic manipulation of the matrix multiplication. In this work, a new approach – the matrix summation approach – is developed and implemented for modelling the geometric errors of five-axis machine tools. This approach breaks down the kinematic equation into six components, each of which has clear physical meaning. It reduces the computations substantially and makes the five-axis kinematic model manageable and understandable.