Abstract: The over-restriction of a parallel kinematic machine (PKM) is simplified and through analysis the 1-differential and 2-differential kinematic equation, the identified parameters among which there are strong relationships are eliminated and it proves that the vertical tolerance along z axis is approximately only related with the non-vertical coefficient of the two columns, so that the parameter errors are classified from the view of output errors. Based on the only relationship of the z axis vertical tolerance, calibration of the PKM is carried out by two steps through a simple scheme about relative position measurement. The results show that in almost all workspace the accuracy is improved to below ±0.04 mm and in partial workspace the accuracy to below ±0.02 mm, so that the industrial requirement is satisfied. The method based on relativity analysis can simplify the calibrating process and identify parameters step by step. Then it gives a new way for PKM calibration.

Key words: Calibration, Error compensation, Parallel kinematic machine, Relativity