**5. Conclusions**

This study applied nonuniform-rational-basis-spline (NURBS) curves for the design of torsion springs, analyzed the displacements of these springs using finite-element analysis, and verified the design of these springs through experimentation.

(1) A method was proposed for deriving the coordinates of a control point for shifted elements by applying the inverse method on the basis of data derived through finite-element analysis. In addition, the relationship between the movement of the control point and stiffness matrix was identified and formulated by varying the torsion-spring parameters.

(2) A method was proposed for deriving the torsion-spring shape by converting the torsion-spring displacement measured through experiments into coordinates that could be expressed using NURBS curves.

(3) Comparative analyses between the results of the proposed analytical method and the experiment measurements demonstrated that the proposed method is valid within a satisfactory range of error.

**Author Contributions:** Y.S.K., Y.J.S., and E.S.J. conceived and designed the experiments; Y.S.K., Y.J.S., and E.S.J. performed the experiments; Y.S.K., Y.J.S., and E.S.J. analyzed the data; Y.S.K., Y.J.S., and E.S.J. contributed reagents/materials/analysis tools; and Y.S.K., Y.J.S., and E.S.J. wrote the paper. All authors have read and agreed to the published version of the manuscript.

**Funding:** This research received no external funding.

**Conflicts of Interest:** The authors declare no conflict of interest
