Applications of equivalent components concept on the singularity analysis of TRR–XY hybrid parallel kinematic machine tools

The design of using a parallel kinematic mechanism as a structure of machine tools has several good points compared with the traditional machine tools. However, the problem of singularity is usually encountered during real applications. Therefore, singularity analysis is very essential for using a parallel kinematic mechanism in real machining applications. Screw theory based on the Plücker coordinate system is one of the effective methods for analyzing the singularity of a parallel kinematic mechanism. A TRR–XY five DOF parallel kinematic machine tool that was developed in this research is adopted as an example for investigating the feasibility of this method. A 6×6 matrix calculation is usually required in screw theory for analyzing a six DOF mechanism. For a three DOF mechanism, the analysis using the screw theory becomes more complicated. An equivalent component method is addressed in this research to simplify the singularity analysis for a three DOF mechanism. The effects of differently designed dimensions of machine tools on the singularity are also investigated in this research.