Probabilistic fasteners with parabolic elements: biological system, artificial model and theoretical considerations

Probabilistic fasteners are attachment devices composed of two surfaces covered with cuticular micro-outgrowths. Friction-based fasteners demonstrate high frictional forces when the surfaces come into contact. Attachment in this case is based on the use of the surface profile and mechanical properties of materials, and is fast, precise and reversible. The best-studied examples composed of parabolic elements are the wing-locking mechanism in beetles and the head arrester in dragonflies. This study combines experimental data of force measurements, obtained in an artificial model system, and theoretical considerations based on the simple model of behaviour of probabilistic fasteners with parabolic elements. Elements of the geometry in both cases correspond to the biological prototypes. Force measurements on the artificial system show that the attachment force is strongly dependent on the load force. At small loads, the increase of attachment is very slow, whereas rapid increase of attachment was detected at higher loads. At very high loads, a saturation of the attachment force was revealed. A simple explanation of the attachment principle is that with an increasing load elements of both surfaces slide into gaps of the corresponding part. This results in an increase of lateral loading forces acting on elements. High lateral forces lead to an increase of friction between single sliding elements. An analytical model which describes behaviour of the probabilistic fasteners with parabolic elements is proposed.