Constant Force Spring System with a Spiral – Part 2: Accuracy assessment

Abstract

The 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 the Journal of Mechanisms and Robotics, vol. 12, December, 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 was solved, and all this is published in that previous paper. That paper contains the detailed description of the theory of the mechanism and the analysisi 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, that is, the force Fo remains not entirely constant during winding/unwinding of the cord. This inaccuracy 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, constitute 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 by Hetnarski [1], before reading the present paper.