Constant Force Spring System With a Spiral: Accuracy Assessment

This paper is an extension of the original research contained in the paper “Constant Force Spring System With a Spiral” by Richard B. Hetnarski, published in J. Mech. Rob., 12, Dec. 2020. The topic of that paper is the introduction and description of a new mechanism which allows to transform the linearly changing force exerted by a helical spring into a constant force. The most important part of the system is a new spiral of which the differential equation was derived and solved, and all this is published in that previous paper. That paper contains the detailed description of the theory of the mechanism and the analysis of its operation. There are also provided examples of a few possible applications. A physical model of the system was built, and its testing showed the system works in agreement with the theory. However, the system is not completely accurate, i.e., the force F_o remains not entirely constant during winding/unwinding of the cord. The present paper deals with this inaccuracy which is discussed and evaluated in depth by analytical and numerical methods, and the way for it to be decreased or eliminated is described. The present paper, together with the previous paper, constitutes the full presentation of the mechanism and should not be separated one from the other. Since the present paper is a continuation of the previous paper, please study the paper (Hetnarski, R. B., 2020, “Constant Force Spring System With a Spiral,” ASME J. Mech. Rob., 12(6), p. 061018. 10.1115/1.4047982), before reading the present paper.