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ARTICLE

# Design of Non-linear Beam-type Spring for Designated Loading and Displacement for Use in Lower-limb Orthosis

Dein Shaw1,2, Chih-Ren Huang2, Li-Cheng Huang2

Tel.: + 886-3-5715131 ext. 42604; Fax: + 886-3-57339979; E-mail: dishaw@pme.nthu.edu.tw
Department of Power Mechanical Engineering, National Tsing Hua University, Hsin Chu, Taiwan, R.O.China

Computers, Materials & Continua 2009, 11(3), 229-242. https://doi.org/10.3970/cmc.2009.011.229

## Abstract

In this study, a method for designing an in-plane, free-form, beam-type spring for use in a lower-limb orthosis was developed. A spring designed by this method follows a predefined relationship between loading and displacement. To facilitate the analysis of the spring, it was divided into several beam segments. The stiffness equations related to loading (including moment and force) and displacements (linear and rotation) of each beam segment were found to follow a modified (non-linear) Castigliano's second theorem (NCST) and were assembled by using the continuity of nodal points of neighbouring curve segments. Using the proposed method, a spring designer can design the spring which has the relationship between the loading and displacement of springs such as those used in lower-limb orthoses. In order to verify the effectiveness of the proposed method, analysis results of deformation of a cantilever spring and cubic spline spring by the finite element method, Castigliano's second theorem, and NCST were compared. Further, an experiment was performed in which the path of motion of the lower limb of a subject climbing up stairs was measured. The results showed that the proposed method was effective and NCST could be successfully used to design the shape of the cubic spline spring.

## Keywords

D. . Shaw, C. . Huang and L. . Huang, "Design of non-linear beam-type spring for designated loading and displacement for use in lower-limb orthosis," Computers, Materials & Continua, vol. 11, no.3, pp. 229–242, 2009.

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