Experiments on vibration-driven stick-slip locomotion: A sliding bifurcation perspective

Dry friction appears at the contact interface between two surfaces and is the source of stick-slip vibrations. Instead of being a negative factor, dry friction is essential for vibration-driven locomotion system to take effect. However, the dry-friction-induced stick-slip locomotion has not been fully understood in previous research, especially in terms of experiments. In this paper, we experimentally study the stick-slip dynamics of a vibration-driven locomotion system from a sliding bifurcation perspective. To this end, we first design and build a vibration-driven locomotion prototype based on an internal piezoelectric cantilever. By utilizing the mechanical resonance, the small piezoelectric deformation is significantly amplified to drive the prototype to achieve effective locomotion. Through identifying the stick-slip characteristics in velocity histories, we could categorize the system's locomotion into four types and obtain a stick-slip categorization diagram. In each zone of the diagram the locomotion exhibits qualitatively different stick-slip dynamics. Such categorization diagram is actually a sliding bifurcation diagram; crossing from one stick-slip zone to another corresponds to the triggering of a sliding bifurcation. In addition, a simplified single degree-of-freedom model is established, with the rationality of simplification been explained theoretically and numerically. Based on the equivalent model, a numerical stick-slip categorization is also obtained, which shows good agreement with the experiments both qualitatively and quantitatively. To the best of our knowledge, this is the first work that experimentally generates a sliding bifurcation diagram. The obtained stick-slip categorizations deepen our understanding of stick-slip dynamics in vibration-driven systems and could serve as a base for system design and optimization.