Jumping insects and hoops : biologically inspired dynamics of small jumpers on water and deformable solids

다국어 초록 (Multilingual Abstract)

Jumping is used by animals as an efficient means of locomotion to escape predators, to catch prey, to increase their speed, or to launch into flight. Small arthropods such as froghoppers, crickets, fleas, grasshoppers, spiders and water striders are able to jump many times their body lengths. Inspired by the superior maneuverability of those insects, biomimetic robots, which mimic the structures, functions and designs of living creatures, are being developed with the goal to jump on land and water. In this study, we combine experimental observation and theoretical analysis to obtain the fundamental understanding of the mechanics of jumping of an articial jumper and insects on various environment. We started with bio-inspired, simple artificial system jumping on rigid solids, deformable solids, and water, and then move on to the living creatures, grasshoppers and water striders, jumping on leaves and water.
We first consider an elastic hoop as a simple jumper mimicking insects jumping, which can store elastic strain energy in its body structure to propel itself. We investigate the jumping dynamics of the elastic hoop on various substrates as a model of the jumps of small insects. During a jump the initial elastic strain energy is converted to translational, gravitational, and vibrational energy, and is dissipated by interaction with the substrate and the ambient air. We show that the energy transfer ratio from initial strain energy to translational kinetic energy of hoop depends on the interaction with the substrate which it launches on. When it jumps on rigid solids, the strain energy is initially divided into translational, vibrational, and dissipation energies with a ratio that is constant regardless of the dimension, initial deflection, and the properties of a hoop material. In contrast, when it jumps on deformable substrates such as flexible solids and liquid surface, the energy transfer rate differs depending on the deformation characteristics of the substrates with respect to the hoop properties. This novel result enables us to accurately predict the maximum jump height and efficiency of a hoop with known initial conditions and drag coefficient without resorting to a numerical computation. Our model reduces the optimization of the hoop geometry for maximizing the jump height to a simple algebraic problem.
Next, we focus on the strategy of living creatures jumping on deformable substrates; how how grasshoppers control jump on stems with various mass and stiffness, and water striders can jump on water so elegantly. We observe and measure jumps of different species of grasshoppers on artificial stems and water striders on water, and then analyze them mathematically. When they jump, grasshoppers make thrust by virtue of inertial and bending stiffness of stems, whereas water striders exploit capillary force from the water surface which serves the most efficient propulsion on water. We experimentally find an evidence that different species of grasshopper control the power as per the substrate on which they launch. We also find that the leg stroke speeds of different species of striders correspond to the mathematically calculated optimal values to maximize the takeoff velocity by fully exploiting the capillary force of water. This implies that the jumping striders always tune their leg rotation speed to reach the maximum jumping height that water surface allows. Our mathematical model extracts the essential variables of insect jumping to be useful with further research.
Our work provides a mechanistic understanding how the animal achieves such a dramatic and powerful motion and how artificial jumpers perform on deformable substrates including liquid, as an essential starting point to develop biomimetic semiaquatic microrobots and robots traveling tough terrain with vegetation. Moreover, this findings raise a question whether such a capability of the insect (optimized behavioral trait and morphology) is a result of evolution or learning, which is hoped to stimulate further research.

목차 (Table of Contents)

• 1 Introduction 1
• 2 Bio-inspired jumping hoops on various substrates 3
• 2.1 Introduction 3
• 2.2 Jumping of an elastic hoop on a rigid solid 4
• 2.2.1 Experimental methods 5
• 2.2.2 Jumping height without air drag 7
• 2.2.3 Jumping height with air drag 10
• 2.2.4 Optimization of hoop geometry 11
• 2.3 Jumping of an elastic hoop on flexible solids 17
• 2.3.1 Experimental methods 18
• 2.3.2 General features of jumping on basal hoops 18
• 2.3.3 Takeoff velocity of hoops on basal hoops 21
• 2.3.4 Efficiency of jumping of hoops on basal hoops 26
• 2.4 Jumping of an elastic hoop on water 26
• 2.4.1 Experimental methods 27
• 2.4.2 Hydrodynamic forces of Jumping on water 30
• 2.4.3 Takeoff velocity of hoops on water 30
• 2.4.4 Efficiency of jumping on water 31
• 2.5 Conclusions 33
• 3 Jumping of insects on deformable substrates 36
• 3.1 Introduction 36
• 3.2 Jumping of grasshoppers on artificial stems 37
• 3.2.1 Experimental Methods 37
• 3.2.2 General features of grasshoppers jumping on artificial stems 37
• 3.2.3 Model of jumping locomotion of grasshoppers 38
• 3.2.4 Dynamic analysis of jumping grasshoppers on artificial stems 40
• 3.2.5 Advantages of grasshoppers locomotion in jumping on stems 42
• 3.3 Jumping of water striders on water 47
• 3.3.1 Experimental Methods 47
• 3.3.2 General features of water striders jumping on water 47
• 3.3.3 Hydrodynamic forces on the water striders legs 49
• 3.3.4 Model of locomotion of water striders jump 52
• 3.3.5 Criteria for exploiting the water surface 54
• 3.3.6 Dynamic analysis of jumping water striders on water 56
• 3.3.7 Types of jumping and the regime map 59
• 3.3.8 Advantages of water striders locomotion in water jumping 63
• 3.3.9 Relation between water striders morphology and water jumping 66
• 3.4 Conclusions 67
• 4 An integrative view of artificial and natural small jumpers on deformable substrates 70
• 4.1 Equivalent models of water to deformable substrates 70
• 4.2 An integrative map of efficiency of jumping on deformable substrates 71
• 5 Conclusions 73