The Effect of Nonlinear Springs in Jumping Mechanisms

Abstract

This research investigates the potential effects of utilizing nonlinear springs on the performance of robotic jumping mechanisms. As a theoretical example, we study dynamic characteristics of a jumping mechanism consisting of two masses connected by a generic nonlinear spring, which is characterized by a piecewise linear function. The goal of this study is to understand how the nonlinearity in spring stiffness can impact the jumping performance. To this end, non-dimensional equations of motion of the jumping mechanism are derived and then used extensively for both analytical and numerical investigations. The nonlinear force-displacement curve of the spring is divided into two sections: compression and tension. We examine the influences of these two sections of spring stiffness on the overall performance of the jumping mechanism. It is found that compression section of the nonlinear spring can significantly increase energy storage and thus enhance the jumping capabilities dramatically. We also found that the tension section of the nonlinear force-displacement curve does not affect the jumping performance of the center of gravity, however, it has a significant impact on the internal oscillations of the mechanism. Results of this study can unfold the underlying principles of harnessing nonlinear springs in jumping mechanisms and may lead to the emergence of more efficient hopping and jumping systems and robots in the future.