Generalized kinematics of five-axis serial machines with non-singular tool path generation

• Screw theory based generalized forward and inverse kinematics of five axis machine tools are presented.
• Tool tip and tool orientation positions are splined with smooth C3 continuity.
• Tool path singularities are avoided by local deformation of tool orientation splines without violating path tolerance.

Typical five-axis machine tools have three translational and two rotary drives. This paper presents a generalized kinematics model that allows automatic configurations of all five-axis machine tools using screw theory. First, each kinematic element is modelled as a revolute joint, prismatic joint, workpiece or cutting tool. The kinematic elements are mathematically assembled through screw theory by using the base coordinate system. The general inverse kinematics solutions for both rotary and translational motions are evaluated. The singularities in five axis contouring are avoided by deforming splined tool orientation vectors. The tool orientation vectors are represented by a fifth degree B-spline curve in a quaternion space, while the movement of tool tip is represented by a fifth degree B-spline curve in the Cartesian space. Both splines, which form the C3 continuous tool path, are fitted to curve length parameter of the tool tip positions. If the tool path traverses the singular area of the machine, it is deformed by modifying the control points of the tool orientation spline in the quaternion space while respecting the machining tolerance. The proposed kinematics module, tool path generation algorithm and method for avoiding kinematic singularities are experimentally verified on a five-axis machine tool controlled by an in-house developed CNC system.