Optimum Design of Balancing Systems with Cylindrical Helical Extension Springs

The static balancing of the weight forces is necessary to any mechanical system which is not working in horizontal plane. The effect is the decrease (until to vanishing) of the acting power. From practical point of view two main ways of static balancing could be taken into consideration: by mass redistribution of components or/and by adding counterweights, and by elastic forces of the springs or of the gases. The first solution is not always possible due to the dimensions of mechanical systems and due to increasing of the dynamic stresses of components. Second solution is more and more used to various mechanical systems.The complexity of balancing systems with springs comes from the need of using zero-free length springs. In any case the mathematical model has not a unique solution. Present paper is an extension of a paper of first author [1] and is presenting a method to find the optimum solution of the simplest elastic system which is using a real helical extension spring with finite-free length. Design variables are the position of spring’s joints, as well as the constructional parameters of a extension spring. Finally some examples are presented.