Constant-force springs are frequently used for such fields as our daily life and engineering, where constant forces or torques are needed. The shatter for garage is a typical example for the former, and holders to keep tool’s position, where workers want, is another for the latter. The fundamental analyses for constant force springs had been developed for more than 60 years ago by well-known F. A. Votta. His theory based on the energy method tells us that the forces produced by springs are always constant regardless of the number of wound spring around a drum. The authors need, however, to discuss exactly about the characteristic of the constant force spring, when the relation between the spring force and the stroke is required to be accurately obtained. In this paper, the authors aim at deriving an additional idea to Votta’s theory, which is taken the number of turns into consideration. It is clarified in this paper that (1) Results obtained analytically from both equations by the authors and Vottas’ are bigger by round 10% than experimental ones, (2) Exactly saying, the spring forces increase with increment of the stroke and (3) The spring force may be reduced dramatically at the inverse of square of the radius of free spring. The authors point out additionally that there is a serious mistake in the well-known Votta’s equation regarding to the rigidity of plate.
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