Fig. 1. Slow tool servo turning lathe

Fig. 2. Tool turning path. (a) Constant-angle method; (b) constant-arc method

Fig. 3. Cutting points distribution of freeform surface. (a) Coordinate system of cutting points; (b) cutting path distribution

Fig. 4. Ideal and actual cutting trajectories

Fig. 5. Schematic of linearization error. (a) Difference between the actual cutting path and the ideal cutting path;(b) linearization error value

Fig. 6. Expansion curve of cutting path. (a) Constant-angle method; (b) constant-arc method

Fig. 7. Freeform surfaces and linearization error curves. (a)(d)(g) Surfaces of XY polynomial, Zernike polynomial, and sinusoidal grid; (b)(c) XY polynomial linearization error curves of constant-arc and constant-angle methods; (e)(f) Zernike polynomial linearization error curves of constant-arc and constant-angle methods; (h)(i) sinusoidal grid linearization error curves of constant-arc and constant-angle methods

Fig. 8. Linearization error curves of constant-arc and constant-angle methods

Fig. 9. Fitting error curves

Fig. 10. Linearization error curves. (a) Constant-arc and constant-angle methods; (b) fitting error curves; (c) error curves of the combination method

Fig. 11. Optimization effect of tool path generation. (a) Tool path optimization of X-Y plane; (b) partial enlargement of the tool path; (c) tool path optimization of sinusoidal grid surface