Fig. 1. Schematic diagram of double revolving （left） and R-θ （right）

Fig. 2. R-θ fiber unit motion schematic

Fig. 3. Rough and precise positioning diagram

Fig. 4. Schematic diagram of coarse positioning

Fig. 5. Schematic diagram of straight circular flexible hinge

Fig. 6. Schematic diagram of lever magnifying mechanism

Fig. 7. Influence of hinge thickness and arc radius on rotational stiffness

Fig. 8. Assembly diagram of lever magnifying mechanism

Fig. 9. Relationship between the driving force and the input and output displacement

Fig. 10. Stress distribution diagram of the flexible hinge when the driving force is 23 N

Fig. 11. Hysteresis nonlinearity of output displacement of amplifying mechanism

Fig. 12. Hysteresis factor （left） and Preisach plane （right）

Fig. 13. Voltage traces on the S-plane

Fig. 14. Discretized Preisach plane

Fig. 15. Schematic diagram of the first-order gyration curve

Fig. 16. Experimental test of the lever magnifying mechanism

Fig. 17. Graph of the F-function

Fig. 18. Applied voltage sequence and actual test displacement of the group one

Fig. 19. Model calculated displacement and error plots of the group one

Fig. 20. Applied voltage sequence and actual test displacement of the group two

Fig. 21. Model calculated displacement and error plots of the group two

Fig. 22. Applied voltage sequence and measured displacement of the group three

Fig. 23. Applied voltage sequence and actual test displacement of the group three

Fig. 24. Absolute mean error varies with the constant C

Fig. 25. Error distribution diagram of positive model before and after optimization

Fig. 26. Expected displacement and calculated voltage sequence of the group one

Fig. 27. Inverse model error distribution of the group one

Fig. 28. Expected displacement and calculated voltage sequence of the group two

Fig. 29. Inverse model error distribution of the group two

Fig. 30. Expected displacement and calculated voltage sequence of the group three

Fig. 31. Inverse model error distribution of the group three

Fig. 32. Search strategy 1

Fig. 33. Search strategy 2

Fig. 34. Search strategy 3

Fig. 35. Linear schematic diagram