Abstract: Four kinds of curve equation are derived which are caused by the radial error motion F(t) of master sphere center and g——harmonic Fg(t) of F(t). The equations indicate characteristic of spindle radial plane motion. They are expressed in vector form, this will make the geometric analysis of the curves more convenient. The geometric relationship between stationary and moving centrodes(both are circles)produced by Fg(t) of F(t) ——inside tangency or outside tangency, and the shape of rotary curves---hypocycloid or epicycloid are demonstrated. It is expounded that as long as F(t) is picked, rotary curve of any point can be accurately obtained, therefore mechining roundness error of machine tools can be correctly forecasted and evaluated.

Key words: Geometric, Harmonic, Precision, Spindle