The main purpose of springs is to utilize their elasticity, and accurately understanding the relationship between load and deformation is a fundamental and important issue in industry. In general, springs show unexpectedly large deformations even when subjected to small loads, so it is difficult to accurately analyze such large deformation behavior by using the conventional small deformation linear theory, and precise nonlinear analysis is required. Incidentally, spiral bellows and zigzag springs (also known as S-springs), which are used, for example, as springs to support car seats and sofas, have a complex shape that combines arc sections and straight sections, and the arc sections are basically semicircular (180°). This paper deals with innovations in the deformation characteristics of such semicircular zigzag springs (S-springs) from a mechanical point of view, and in this paper, a new, so-called non-semicircular zigzag spring (S-spring) whose arc sections are not semicircular is assumed with pitch changes in mind. In other words, a new analysis was carried out on the deformation performance of zigzag springs (S-springs) with an arc greater than a semicircle (> 180°) and smaller than a semicircle (< 180°) when the tip is supported in a rotation fixed and a horizontal tensile or compressive load is applied to the supported end. Originally, semicircular zigzag springs (S-springs) exhibited nonlinear large deformation behavior due to loads, but the deformation characteristics of the assumed innovative non-semicircular zigzag springs (S-springs) also have nonlinearity similar to the conventional semicircular zigzag springs. This large deformation behavior has also been newly analyzed by using nonlinear theory, and analytical solutions by using elliptical integrals have been given for some representative deformation quantities. Furthermore, the deformation characteristics of conventional semicircular zigzag springs (S-springs) have mainly been analyzed by using small deformation linear theory, but the authors were the first to perform an actual large deformation analysis. The merit of this research is that it is the first in Japan to attempt an innovation in semicircular zigzag springs (S-springs), and it has clarified the large deformation behavior of the innovative zigzag springs, revealing guidelines for improving the performance and accuracy of zigzag springs. In addition, this paper presents a generalized theory of large deformation analysis for zigzag springs (S-spring) with various circular arc sections. Semicircular zigzag springs (S-spring) (180°) are recognized as a special example.
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