Abstract
A model for serpentine locomotion is derived from a novel perspective based on concepts from configurational mechanics. The motion is realized through the release of the elastic energy of a deformable rod, sliding inside a frictionless channel, which represents a snake moving against lateral restraints. A new formulation is presented, correcting previous results and including situations never analysed so far, as in the cases when the serpent's body lies only partially inside the restraining channel or when the body has a muscle relaxation localized in a small zone. Micromechanical considerations show that propulsion is the result of reactions tangential to the frictionless constraint and acting on the snake's body, a counter-intuitive feature in mechanics. It is also experimentally demonstrated that the propulsive force driving serpentine motion can be directly measured on a designed apparatus in which flexible bars sweep a frictionless channel. Experiments fully confirm the theoretical modelling, so that the presented results open the way to exploration of effects, such as variability in the bending stiffness or channel geometry or friction, on the propulsive force of snake models made up of elastic rods.
Highlights
Since the beginning of the research on creeping locomotion, four different mechanisms for snake motion have been identified [1,2,3,4]: serpentine, concertina, side-winding and rectilinear
A special feature characterizes the first of the four movements, namely that the snake has to exert normal forces against projections from the ground1 to induce longitudinal sliding, so that tangential frictional forces operating between the serpent and the terrain have to be minimized, because they oppose gliding forward
The mechanical model of Gray is made up of a chain of rigid pieces connected to each other with rotational springs, while a more refined model in which a snake is represented by an elastic rod (Euler’s elastica; see, for instance, [9 –11]) has been introduced in an almost unknown article by Kuznetsov et al [12], based on results presented in another forgotten article by Lavrentiev and Lavrentiev [13]
Summary
Since the beginning of the research on creeping locomotion, four different mechanisms for snake motion have been identified [1,2,3,4]: serpentine, concertina, side-winding and rectilinear. The propulsive force is independently derived using two approaches: (i) an energy formulation and (ii) an approach based on the ‘micromechanical’ derivation of all forces acting on the system, enhanced by the integration of the equations of motion These two approaches have different merits, so that only the knowledge of both provides a complete picture of serpentine motion through a perfectly smooth channel. The micromechanical approach shows that the perfectly frictionless channel provides propulsion by means of tangential localized reactions acting against the snake’s body This is a surprising behaviour, counter-intuitive from a mechanical point of view. The presented experiments are limited to a channel in the form of a clothoid spiral and to three different types of elastic rods, the methodology introduced allows exploration of more complex situations, for instance involving friction at the rod/channel contact or sophisticated variability in the snake’s bending stiffness or channel geometry
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