Error separation is a key technology for online measuring spindle radial error motion or artifact form error, such as roundness and cylindricity. Three time-domain three-point error separation methods are proposed based on solving the minimum norm solution of the linear equations. Three laser displacement sensors are used to collect a set of discrete measurements recorded, by which a group of linear measurement equations is derived according to the criterion of prior separation form (PSF), prior separation spindle error motion (PSM) or synchronous separation both form and spindle error motion (SSFM). The work discussed the correlations between the angles of three sensors in measuring system, rank of coefficient matrix in the measurement equations and harmonics distortions in the separation results, revealed the regularities of the first order harmonics distortion and recommended the applicable situation of the each method. Theoretical research and large simulations show that SSFM is the more precision method because of the lower distortion.
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