to be found in outer space but also commanding space on earth. The deployment ... (From an original drawing by B. Kresling). Fig. ... and, while the blood pressure is generated primarily at the base of the ... bivalve mollusc living in sand, such as a razor shell. Fig. ..... ciplines, avoiding the adaptations due to optimization.
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Deployable structures in nature: potential for biomimicking J F V Vincent Centre for Biomimetics, The University of Reading, TOB 1, Earley Gate, Reading RG6 6AT, UK Abstract: Biology contains many examples of deployable structures. They can be grouped as planar, cylindrical, sti and compliant, and space frame combining both sti and compliant elements (tensegrity structures). Deployment occurs due to high strain elastic materials, or folds and curves that can be actuated by springs, changes in shape (mediated by hydraulic or contractile mechanisms) or changes in stiness. Evolution ®lters out ineciency. Transfer of nature's technology requires understanding of the optimizations in the biological system. The concepts can then be used in aerospace, deployable camou¯age, packaging, emergency shelters, capture systems, etc. Keywords: 1
deployment, biomimicry, aerospace, camou¯age, origami, folding, packaging
STRUCTURES
There are many examples of deployable structures in nature and many apparent reasons for their evolution. For instance, the organism may want to store structures out of harm's way or to reduce inertia so that locomotion can be more eective with reduced muscular eort, or it may need to deploy a structure very quickly, perhaps for power ampli®cation or to grow it protected in a bud. The most familiar deployable structure is your arm which you stretch out; geometrically more complex examples are to be found with ¯owers and leaves, although of course their control systems are far less sophisticated. Although the development of properly engineered deployable structures did not start until satellites became commonplace, they are now not only to be found in outer space but also commanding space on earth. The deployment mechanisms of nature are not newly recognized, but engineering concepts and applications have coloured the way that biological systems can be looked at and have encouraged the reordering of information based on a novel set of functional criteria. This very rede®nition tends to encourage innovation since it brings together concepts that might have remained separate. 1.1
Planar structures
Although many folding patterns can be found in plant structures [1±3], there have been few studies from a The MS was received on 12 May 1999 and was accepted after revision for publication on 24 September 1999. C07899
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mechanical point of view. The leaves of many plants, especially broad-leaved trees of temperate areas, are folded or rolled while inside the bud. For example the leaves of hornbeam and beech have a straight central (primary main) vein and symmetrically arranged parallel lateral (secondary) veins which generate a corrugated surface. The primary vein elongates, separating the bases of the secondary veins and causing the lamina between the secondary veins to rotate into the plane of the leaf, at the same time causing the secondary veins to rotate away from the main vein [4] (Fig. 1). These two mechanisms provide the initial ®fth of the increase in the projected area of the leaf as it expands. Other leaves such as sycamore and maple unfold in a radial manner. In the leaf, the membrane between the veins also expands. The controlling factor here seems to be the orientation of the cellulose micro®brils in the walls of the cells which make the upper and lower surfaces of the leaf (the epidermal cells). In the early expansion phase the cellulose is oriented orthogonally to the direction in which expansion will occur, so that only the material between the cellulose ®bres, of lower modulus, needs to be stretched. When expansion ®nishes, the cellulose ®bres have rotated 90 , thereby stiening the membrane in the expansion direction and stopping the process. The unfolding of ¯ower petals employs a number of mechanisms not found in leaves. A Miura-ori folding pattern (a development of a basic pattern in origami) is evident in poppy petals [2, 5] (Fig. 2); the ¯owers of hollyhock and morning glory use a spiral packing mechanism [6]. Wing folding of insects has also been investigated [7± 9]. The geometry and mechanics of wing folding of coleoptera have been studied using vector analysis [10]. Proc Instn Mech Engrs Vol 214 Part C
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Fig. 1
The geometry of a simple expanding leaf. (From an original drawing by B. Kresling)
Fig. 2 The poppy petal compresses itself as it grows in the bud leading to a naturally induced pleat whose main characteristics are the same as the Miura-ori. (From reference [1])
Although in general the patterns of folding follow simple rules, it is often important for the wing to be bistable in some fashion, since its folding can be controlled only by three hinge points at the base of the wing. It is therefore quite common to ®nd buckling mechanisms built into the wing structure which can both stien the membrane and turn it into a bistable mechanism, Proc Instn Mech Engrs Vol 214 Part C
enabling it to fold and unfold and to remain in either of those states when required. These mechanisms have been identi®ed in general terms but not analysed. At least in part this is because the mechanical properties of the wing membrane and stiening structures, collectively made of a composite of chitin micro®brils in a tanned protein matrix, are unknown. C07899
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Fig. 3 The nematocysts, ready for triggering (left) and discharged (right). The ®lament is longer by a factor of several tens than shown here
1.2
Compliant tubes
One of the commonest deployable tubes is typi®ed by the earthworm (Lumbricus) whose body wall is constructed of crossed-helical windings of collagen ®bres. This links geometrically the length and diameter of the tube if the volume is kept constant. At maximum volume the `solution' is familiar to engineers as the winding angle of ®bres around a pressurized cylinder: 54 450 . Below this volume, shape changes are possible and the double-helical winding takes on the properties of a tubular `lazy tongs' mechanism. A similar structure is found in the body wall of sea anemones which expand and extend above the substrate in order to feed, in the tube feet of sea urchins and star ®sh, which can extend to lengths of several centimetres, and in the wall of the extensible foot of some burrowing bivalves. Sea anemones, corals and jelly ®sh can sting with a hollow thread which is shot out under high pressure from an organelle known as a nematocyst. The thread everts itself as it goes through a combination of folding and lengthwise rotation, like the sleeve of a coat carelessly doed, or the inverted ®nger of a glove [11, 12] (Fig. 3). The thread has barbs and other sharp devices on it and can deliver poison into the resulting wound. The proboscis (feeding tube) of Lepidoptera (butter¯ies and moths) is normally stored as a coiled structure beneath the head of the insect (Fig. 4). When the insect wishes to feed, it uncoils the tube and extends it into the food source (Fig. 5). The elastic mechanism is akin to stretching out a steel measuring tape and allowing it to take up a stier `trough` section to remain extended. Internal blood pressure may play a minor part [13, 14] and, while the blood pressure is generated primarily at the base of the proboscis, it is possible that the volume C07899
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of the proboscis reduces locally as a result of being straightened, generating extra pressure. No pressures have been measured. One advantage of the pressure tube mechanism is that the tube can be `super-uncoiled', allowing the tip of the proboscis, normally pointing downwards, to re¯ex and point upwards, making it easier to guide it into the complex tubes of a ¯ower's nectaries. Modern instrumentation would allow the mechanical properties of the proboscis to be measured, despite its small size, and a more complete analysis to be made. There are several examples of soft extensible tubes, many of which can also be steered like a tensegrity mast (see Section 4). The respiratory tubes or siphons of a bivalve mollusc living in sand, such as a razor shell
Fig. 4
The tightly-coiled proboscis of a butter¯y. This is carried beneath the head. The coil is about 1 mm in diameter Proc Instn Mech Engrs Vol 214 Part C
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Fig. 5 A hawk moth ¯ying to a ¯ower with its proboscis extended. The tip of the proboscis is hyper-uncoiled
(Ensis), allow the animal to remain buried and protected and yet to respire and feed. The siphons extend to the surface of the sand, providing inhalent and exhalent passages. They extend at a constant diameter, implying a low Poisson's ratio in the plane of the wall due to ®bres that are arranged circumferentially. In another example of this type of morphology, the extensible abdomen of the locust, the circumferential sti chitin ®bres give the material a Poisson's ratio of 0.03 at higher extensions [15]. As the tube extends, the ®bres resisting the compressive forces developed in the soft
E 1 kPa) matrix buckle, locally generating kink bands.
1.3
Sti rods and tubes
There are many mechanisms made from the articulation of sti parts; a large part of classical morphological and biomechanical zoology is concerned with their description and classi®cation [16]. Examples are the jaw of the snake, which can dislocate to give an extremely wide gape, various egg-laying devices and drills found in insects [17] and the deployment of limbs. The simplest form of mechanism has four bars hinged to each other. This has been exhaustively analysed in a series of papers by Muller, who has used it to explain the working of the mouth and related apparatus of many species of ®sh [18]. He has presented a novel classi®cation of planar four-bar linkages based on the systematic variation of one, two or three bar lengths and studied the transmission properties (input±output curves) of the linkages. The mechanical features of a wide range of planar linkages in vertebrates, described by various workers, have been included in this classi®cation. Examples are mechanisms in ®shes, reptiles and birds for opening the jaws and pushing them forwards, the coral crushing apparatus of parrot-®shes and catapult mechanisms in feeding pipe-®shes. The most complex system is the protrusion mechanism found in the jaw of the sand-eel, Proc Instn Mech Engrs Vol 214 Part C
Ammodytes tobianus, which consists of a bilateral series of six four-bar linkages. The most spectacular is the fourbar jaw mechanism of the angler ®sh, Lophius (Fig. 6). 1.4
Tensegrity three-dimensional structures
In 1948, Kenneth Snelson and Richard Buckminster Fuller worked together on structures which were `islands of compression inside a sea of tension'. Fuller called the resulting structures by the general name of tensegrity (from tensile integrity) and used it to make steerable masts and other lightweight structures. If the tensile elements are made of rubber, then the structure can be collapsed on itself (Fig. 7) and actuated by a few sti tensile elements. If all the compressive elements are shorter than their Euler buckling length, i.e. `short' struts, then this structure can be very ecient since it adjusts itself so that there are no bending loads, only compressive and tensile. In recent years Ingber and coworkers [19] have suggested that the shape and internal structure of cells are maintained by a tensegrity system. Although Ingber and co-workers have revealed the necessary components, connected in a convincing manner, they do not appear to have made any structural calculations to show whether (for instance) the aspect ratio of the compressive components (microtubules within the cell of diameter 25 nm and of stiness about 2 GPa) falls below the level at which Euler buckling might be expected. Tensegrity in nature, if it exists, is an area ripe for exploration. 2
ACTUATION
The site of actuation, and the optimizations involved in the mechanism, have not been investigated in many systems. On occasion the general area of the actuator can be fairly obvious, for instance in leaves that move C07899
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Fig. 6 Deployment of the mouth in the angler ®sh, Lophius. (From an original drawing by M. Muller)
with a well-de®ned hinge point. However, with other systems such as ¯ower petals, where folds are ¯attened to the point of obliteration, it is more dicult to locate actuation, and the entire structure is presumably responsible. Where the system is made of sti components, the actuator can normally be pinpointed with ease. In a soft hydraulic system such as a worm or the siphon of a mollusc, the actuator will be muscular but may well be distributed around the animal's body.
2.1
Hydraulic mechanisms
The only mechanism which plants have available for movement is the osmotic pressure developed within the cell, acting via the sti cellulose wall which surrounds each cell. The pressure is commonly 1 MPa and can be several times this. The actuator then appears to be at the point of in¯ection, e.g. the area of swollen cells or pulvinus at the base of folding leaves of pea and bean plants, and of mimosa [20]. In a moist warm atmosphere (22±25 C) the small lateral lea¯ets of Desmodium gyrans, a member of the pea family which grows in the damp Ganges plains, make circling movements so quickly that their tips describe a complete circle in 1± 3 min. The terminal lea¯ets of the clover, Trifolium pratense, oscillate in the dark with an amplitude which may exceed 120 , and a period of 2±4 hr. On exposure to light the lea¯ets stop and assume a ®xed light position. The petals of the dandelion, Taraxacum ocinalt, are C07899
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closed in the dark but open when illuminated (Fig. 8). The pulvini of leaves may be aected by several dierent stimuli; the leaves of Mimosa pudica, for example, are set in motion by the action of light and also by the stimulus of a shock and in addition exhibit autonomic movements. However, although the osmotic pressure can provide adequate force, the power output is relatively low, so that some plants and animals have evolved power ampli®cation mechanisms in which elastic strain energy is stored in part of the structure (e.g. a thickened epidermal cell layer) and released when required (e.g. the insect traps on Dionaea, the Venus ¯y trap). The hydraulic capsule (the nematocyst) which powers the sting of coelenterates (sea anemones, corals and jelly ®sh) contains a 2 M salt solution and reaches an internal pressure of 15 MPa before it shoots out the dart in the ®rst phase of stinging, which it does with an acceleration of 40 000g: The nematocyst is a sphere of 5 mm diameter with walls 200 nm thick. At full pressure, the stress in the wall, which is made of a ®brous polymer, collagen, will be 190±375 MPa [21].
2.2
Changing stiness
Insect wings develop as highly folded structures in the pupal or last nymphal stage and are deployed with pressure from the insect's blood system when the adult has emerged from the pupal cuticle. It is commonly thought that the wings are expanded by the insect Proc Instn Mech Engrs Vol 214 Part C
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after which the folds are ¯attened and resistance to extension increases. This degree of folding accounts for almost all the extension observed. Once ¯attened, the cuticle rapidly becomes ten times stier and twice as strong. These changes in stiness are under the control of the cells which secrete the membrane since the process of expansion can be halted by treatment with cyanide. The insect system is sensible from an energy point of view since the insect is not dissipating energy by pumping blood from its body cavity down small tubes in the wing at a pressure high enough to cause the wing to expand. If this were the mechanism, the rate of extension of the wing would be expected to fall o with the square of the distance of the expanding zone from the base of the wing. This does not happen; the wing continues to expand at almost the same rate until the process is completed. The pressure for further expansion must therefore be generated by the part of the wing which has already expanded and ¯attened, bringing the upper and lower membranes of the wing into contact, thus reducing the space between them. This reduction in volume, and the associated stiening of the membrane, must be sucient to generate the necessary pressure. In more general terms, the changes in stiness by controlling the cross-linking of the material, can actuate a mechanism. Indeed, muscular contraction has been modelled as a change in stiness. In a partially stretched material, an increase in stiness will result in a lower strain at the same stress, thus producing contraction. This mechanism can apply in any material where stiness can be a variable, e.g. many polymers, especially those which can reversibly form liquid crystalline structures, and in the connective tissue of sea urchins, brittle stars, star®sh and sea cucumbers.
2.3 Fig. 7
Simple tensegrity structures: thick lines are struts; thin lines are tensile
actively pumping them up, but this is not the case. A wing can be cut o the insect before it has expanded and, so long as the cut end is sealed, will expand fully in more or less the same time as the attached wing [22]. Therefore the expansion of the wing occurs at constant volume! The unexpanded wing is like a bag which has been crumpled; the walls are highly folded so that most of the extension can come from ¯attening out the folds (Fig. 9). The folded cuticle is initially relatively sti and elastic with an ultimate strain of only 0.3. Within 10 min of the insect's emerging the modulus of the folded cuticle has dropped by an order of magnitude giving it a twophase force±strain curve (Fig. 10). The folds allow the wing to be stretched plastically by a factor of about 2.5, Proc Instn Mech Engrs Vol 214 Part C
Elastic mechanisms
Small animals use spring mechanisms for jumping so that they can deliver all their pent-up muscular energy before their (necessarily short) legs leave the ground [23]. The muscles simply cannot contract quickly enough. In insects the strain energy is stored in resilin or strips of cuticle, which can be compressed (in the ¯ea) or stretched (in the locust) or wound and unwound like a clock spring (which happens in the large thighs of ¯ea beetles and their relatives [24]). Since the energy can be released much more quickly from these springs than from muscle, they act as power ampli®ers and literally catapult the insect into the air by deploying the hind legs. The Venus ¯y trap, Dionaea, lives in peat bogs which are relatively poor in nutrients. In order to supplement its nitrogen intake it traps insects by snapping the lamina of a modi®ed leaf around them. Recent work in our laboratory has shown that this movement can occur in 40 ms or less, far too quick to be due to a change in turgor pressure of the cells in the leaf. The solute content C07899
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Fig. 8 Flower head of a dandelion, closed when kept in darkness and open when illuminated. (From reference [20])
of the leaf cells does not change before and after closing, nor does the stiness of the cell walls. However, the leaf reverses its curvature in closing, and so could be an anticlastic bistable based on a sandwich panel which is
pre-stressed [25], in this instance by turgor in the leaf cells. Cells in the middle layer are thin walled, large and extensible. The upper epidermis is much thicker than the lower epidermis so that the closed state is mechanically more stable than the open state. It seems likely that, once the trap has closed, the changed strains in the cells are mechanically con®rmed by speedy osmotic equilibration. A closed trap can be forced to open again, simply by levering the leaf laminae apart. It takes up to 1 kgfn force to do this but by this time the forces controlling the shape have been changed. The return path to the open leaf takes longer and involves growth. 2.4
Fig. 9
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Isolated locust wing, sealed with wax (stippled) taken from a locust which was moulting into the adult (winged) stage. Labels show the time after the insect ®rst started to split its old skin: stage a, 20 min; stage b, 33 min; stage c, 36 min; stage d, 38 min; stage e, 47 min. The main wing vein is indicated. The slightly irregular outline is due to the crumpling of the wing as it pushes along the surface upon which it is resting. (From reference [22]) ß IMechE 2000
Contractile mechanisms
Muscle is too well known as an actuator to need to be mentioned in such a short review as this. There are other actuators which use a dierent mechanism; an example is spasmonin which occurs in the stalk or spasmoneme of some single-celled animals (e.g. Vorticella) about 1 mm long. Unlike muscle, it is not a sliding ®lament mechanism but depends on the addition of calcium [26]. The maximum instantaneous power of the spasmoneme is 2.7 kW/kg of wet weight which exceeds the average power of the most energetic striated muscles, those involved in ¯ight of insects, which have values in the range 0.05±0.2 kW/kg. The spasmoneme is therefore a high-output mechanochemical engine. It is quite likely that there are other contractile mechanisms in nature that have not been explored. 3
BIOMIMICKING
Before seeing whether any of the mechanisms described has the germ of usefulness, it would be useful to Proc Instn Mech Engrs Vol 214 Part C
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Fig. 10 Load±strain curve of the folded section of the wing: 1, immediately after the insect has escaped from its old skin (stage a in Fig. 9); 2, at the start of wing expansion (just before stage b in Fig. 9). (From reference [22])
understand not only the reasons why it might be useful to abstract an idea from the living world but also the process by which this might be done. The underlying rationale is common amongst both biologists and engineers: expense. How much does it cost to design, to make, to maintain and ®nally to recycle, a structure? For engineering structures and materials this is a cash cost, and the lowest believable tender wins the contract. For living organisms the cost is energy, and the competition is not that of the commercial market-place, but the more severe one of nature, where the ®ttest (cheapest?) survive and where failure equates to death. The process is based on the idea that the entire world, living and non-living, is subject to the same `laws' of physics and mathematics. This level then forms a common ground for the transfer of information between the disciplines, avoiding the adaptations due to optimization. Plicate structures such as the simple leaves of hornbeam and beech oer ideas for easily deployed roo®ng or umbrellas. Unlike the radial actuation of the traditional umbrella and its derivatives, a cover based on the leaf could be deployed and supported from a single extending strut. In a radial leaf, experimentation shows that it can be actuated from a single fold. Concepts based on folded insect wings would probably be rather more dicult to implement since the wing is actuated only from the base; therefore there may be inertial problems. However, some of the locking mechanisms, based on control of elastic buckling, may well prove interesting. They remain to be analysed in natural systems. The tube of the nematocyst oers some intriguing Proc Instn Mech Engrs Vol 214 Part C
possibilities, especially in the medical world where a deployable tube could be used as a stent, which is a tube used to hold open a duct, vein or artery. Since the nematocyst tube deploys very quickly and without snagging, its geometry must be suitable for the sort of remote control that modern surgery demands. Something like the butter¯y proboscis is already widely used in aerospace for deployable antennae where they are known as tape springs. A long strip of steel with a trough-shaped section, like a steel tape measure, is folded by ¯attening the cross-section and rolling it up on a drum. This structure has not been arrived at by copying nature. One of the problems with the tape spring is its stability, since a structure which has been folded in this manner is in a high-energy unstable con®guration and has to be kept within a deployment mechanism which prevents it from jumping towards more stable con®gurations. Another problem is the deployment mechanism, which can be heavier and more complex than the antenna itself. A bistable version of this mechanism has the tape of composite construction with ®bres at 45 and ÿ45 to the long axis [27], relying on a strain energy minimum between the two states to keep each state stable. The biological version of this type of structure is stable in the coiled conformation and appears to require energy input (directly muscular? hydraulic?) to keep it extended. Pneumatic structures, the closest that technology routinely gets to the hydraulic structure of plants and molluscs, have been studied for some 40 years but have not been successful in general structural uses, despite the C07899
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excellent insulation properties of air, the minimal use of materials and the lightweight and cheap construction methods. They are dicult to design and non-linear, they cannot take high loads, and suitably strong hardwearing fabrics are not available. Early in¯atable structures tended to be over-symmetrical, repetitive in form and dull to look at and they acquired a reputation for unpredictability. Modern computer techniques using ®nite elements, developed for the design of tensile structures, are opening the way for the design of deployable pneumatic structures which can be more exciting than the average bouncy castle. A concept that does not seem to have been explored, which occurs more frequently than might be thought in nature, is using hydraulic pressure to store strain energy in an elastic component. This is the underlying principle of the Venus ¯y trap and very probably in other micromechanisms involved with pollination, e.g. in orchids where a mechanism in the pollen-bearing part of the ¯ower bends over and sticks on to the back of a visiting insect. The elastic energy store is the cellulose in the walls of the cells containing the pressurized liquid; the liquid is more or less incompressible. This approach has the advantage of power ampli®cation, so that the strain energy can be accumulated at a low work rate and released suddenly. This would be useful to power an intermittently working deployment mechanism where power is at a premium, e.g. on board a satellite. Deployable structures have been studied for use in aerospace [28]. A two-dimensional expandable array was proposed by Miura for a solar panel whose folding pattern has been called `Miura-ori'. A thin membrane wrapped around a central hub was examined by Guest and Pellegrino [6] as a design for a solar sail. Several concepts of deployable aerospace structure have been described [5]. It is not clear whether these concepts are biomimetic. The likelihood is that they are not, although the structures can be seen in the petals of various ¯owers (poppy, hollyhock and columbine) while they are still in the bud. 4
. . . AND FINALLY
It is all very well looking to nature for inspiration, but there are very few instances of successful transfer of technology. The cynical would say that this is because nature's technology is trivial or that the mechanisms cannot be translated. The diculty in understanding what is happening in many of these systems is emphasized by the non-analytical approach in this paper, which is imposed by our lack of understanding. The hopeful would say that natural mechanisms have their own optimizations which create design hurdles that are conceptual rather than real. The present author's view is that ideas can come from anywhere. While it is very likely that our recognition of a mechanism of technical C07899
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9
utility is seeded within engineering, aspects of implementation and ®ne tuning will be enhanced by study of other versions of the mechanism, including those in nature developed under the rigorous demands of evolution. The umbrella and the rescue dinghy required painstaking and subtle design. Nature can be just as subtle, and with its help perhaps some of the pain can be avoided! REFERENCES 1 Delarue, J. M. Minimal folding con®gurations. In Proceedings of the Second International Symposium, Sonderforschungbereich 230, Part 2, Stuttgart, 1991, pp. 31±41. 2 Kresling, B. Folded structures in natureÐlesson in design. In Proceedings of the Second International Symposium, Sonderforschungbereich 230, Part 2, Stuttgart, 1991, pp. 155±161. 3 Kresling, B. Plant `design': mechanical simulations of growth patterns and bionics. Biomimetics, 1995, 3, 105± 120. 4 Kobayashi, H., Kresling, B. and Vincent, J. F. V. The geometry of unfolding tree leaves. Proc. R. Soc. Lond. B, 1998, 265, 147±154. 5 Miura, K. Concepts of deployable space structures. Int. J. Space Structs, 1993, 8, 3±16. 6 Guest, S. D. and Pellegrino, S. Inextensional wrapping of ¯at membranes. In Structural Morphology, Montpellier, 1992, pp. 203±215. 7 Wootton, R. J. Support and deformability in insect wings. J. Zool., Lond., 1981, 193, 447±468. 8 Kesel, A. B. The insect wingÐa multifunctional mechanical system. In Proceedings of the Third International Symposium, Sonderforschungbereich 230, Stuttgart, 1994, pp. 181±184. 9 Brackenbury, J. H. Wing folding and free-¯ight kinematics in Coleoptera (insects): a comparative study. J. Zool., Lond., 1994, 232, 253±283. 10 Haas, F. Geometry and mechanics of hind-wing folding in Dermaptera and Coleoptera. MPhil thesis, University of Exeter, 1994. 11 Skaer, R. J. and Picken, L. E. R. The pleated surface of the undischarged thread of a nematocyst and its simulation by models. J. Expl Biol., 1966, 45, 173±176. 12 Watson, G. M. and Mariscal, R. N. Ultrastructure of nematocyst discharge in catch tentacles of the sea anemone Haliplanella luciae (Cnidaria: Anthozoa). Tiss. Cell, 1985, 17, 199±213. 13 BaÈnziger, H. Extension and coiling of the lepidopterous proboscisÐa new interpretation of the blood pressure theory. Bull. Soc. Ent. Suisse, 1971, 43, 225±239. 14 Hepburn, H. R. Proboscis extension and recoil in Lepidoptera. J. Insect Physiol., 1971, 17, 637±656. 15 Vincent, J. F. V. The morphology and ultrastructure of the intersegmental membrane of the female locust. Tiss. Cell, 1981, 13, 831±852. 16 Alexander, R. McN. Animal Mechanics, 1983 (Blackwell Scienti®c Publications, Oxford). 17 Vincent, J. F. V. and King, M. J. The mechanism of Proc Instn Mech Engrs Vol 214 Part C
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drilling by wood wasp ovipositors. Biomimetics, 1996, 3, 187±201. Muller, M. A novel classi®cation of planar 4-bar linkages and its application to the mechanical analysis of animal systems. Phil. Trans. R. Soc. Lond. B, 1996, 351, 689±720. Stamenovic, D., Fredberg, J. J., Wang, N., Butler, J. P. and Ingber, D. E. A microstructural approach to cytoskeletal mechanics based on tensegrity. J. Theor. Biol., 1996, 181, 125±136. Strasburger, E., Noll, F., Schenck, H. and Schimper, A. F. W. A Text-Book of Botany, 1903 (Macmillan, London). Holstein, T. W., Benoit, M., Herder, G. V., Wanner, G., David, C. N. and Gaub, H. E. Fibrous mini-collagens in Hydra nematocysts. Science, Wash., 1994, 265, 402± 404. Glaser, A. E. and Vincent, J. F. V. The autonomous in¯a-
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tion of insect wings. J. Insect Physiol., 1979, 25, 315±318. 23 Bennet-Clark, H. C. and Lucey, E. C. A. The jump of the ¯ea. J. Expl Biol., 1967, 47, 59±76. 24 Ker, R. F. Some structural and mechanical properties of locust and beetle cuticle. DPhil thesis, University of Oxford, 1977. 25 Jeronimidis, G. and Parkyn, A. T. Residual stresses in carbon ®bre±thermoplastic matrix laminates. J. Composite Mater., 1988, 22, 401±415. 26 Katoh, K. and Naitoh, Y. Control of cellular contraction by calcium in Vorticella. J. Expl Biol., 1994, 189, 163±177. 27 Daton-Lovett, A. An extendible member. PCT application PCT/GB97/00839, 1996. 28 Unda, J., Weisz, J., Rivacoba, J. and Urfen, I. R. Family of deployable/retractable structures for space application. Acta Astronomica, 1994, 32, 767±784.
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