Morphology and action of the hind leg joints controlling jumping in froghopper insects

Froghopper insects (Hemiptera, Cercopoidea) can launch themselves into a jump in less than 1 ms, achieving take-off velocities of 4.7 m s^-1and experiencing an acceleration of more than 550 g(Burrows, 2006) that propels them to a height of about 115 times their body length(Burrows, 2003). The key movements of the hind legs in generating these movements are the rapid depression of the trochantera about the coxae, accompanied by extension of the tibiae about the femora. The hind legs are, however, only about half the length of the body, indicating that the mechanical advantages to be gained by using long levers (Alexander,1995) are not exploited by froghoppers in jumping. The force requirement for a jump is much greater than could be provided by direct muscle contractions in the brief time (less than 1 ms) that the acceleration is applied. Short hind legs coupled with the intrinsic limitations of muscle suggest that a catapult mechanism must be used. This, in turn, implies that there must be anatomical specialisations of the hind legs to allow force to be generated slowly, whilst they remain stationary, and then to be delivered suddenly to produce a rapid and powerful movement.

Many insects that jump have accompanying specialisations of their limbs,joints, muscles and motor patterns that allow rapid movements to be generated. These specialisations are most marked in the hind legs that generate the propulsive force. Fleas power their jumps by contracting the enlarged trochanteral depressor muscles and storing energy in resilin(Bennet-Clark and Lucey, 1967; Rothschild and Schlein, 1975; Rothschild et al., 1972). The stored force is released apparently by the contraction of a small muscle that changes the point of action of the depressor muscle so that the short hind legs can be depressed rapidly. Flea beetles have enlarged hind femora each containing a spring formed by the curling and chitinisation of the extensor tibiae tendon (Furth, 1988; Maulik, 1929). The tibia is probably locked into the flexed position when a small triangular plate at the femoro-tibial joint is moved by contraction of the flexor muscle and is released in a jump by changes in the flexor force and as the spring snaps back to its original shape.

Grasshoppers have hind legs that are both long and robust with femurs that are 10 times the mass of those of the other legs. The contractions of the large extensor tibiae muscle within the femur distort the femoral cuticle and bend highly sclerotised semi-lunar processes at the femoro-tibial joint, so storing energy to provide the propulsive force for a jump(Bennet-Clark, 1975; Burrows and Morris, 2001). The tendon of the small flexor tibiae muscle has a pouch that engages with a femoral lump that changes the line of action of the tendon as the tibia flexes(Heitler, 1974). These specialisations restrain movements of the tibiae while the large extensor muscles contract slowly before a jump. False stick insects (Orthoptera,Proscopiidae) have long hind legs with curved tibiae, but still require energy to be stored before a jump. The semi-lunar processes on the femora are much reduced and are not bent before a jump, but the tibiae themselves do bend(Burrows and Wolf, 2002). Again, complex arrangements of the lever arms ensure that the small flexor tibiae muscle can restrain the contractions of the larger extensor before the tibia is rapidly extended to power a jump. Both of these insects combine an ability to store energy in advance of a jump and then release it suddenly,with the beneficial effects of long legs as levers. Bush crickets, however,seem to rely more heavily on the leverage from their exceptionally long hind legs so that some jumps are powered by direct muscle contractions acting on long levers (Burrows and Morris,2003).

This paper examines the specialisations of froghopper hind legs that make possible their extraordinary jumping ability. It focuses on the structure and actions of the coxo-trochanteral joint of a hind leg, the rotation of which is the key action in generating rapid jumping movements(Burrows, 2006). It describes the structure and articulation of this joint, possible proprioceptors that monitor its movements and the lever arms of its depressor and levator muscles. It demonstrates how a novel locking mechanism between the femur and the coxa might enable the trochanteral depressor muscle to contract slowly without moving the leg and then suddenly release the rapid jumping movement.

Froghoppers Aphrophora alni (Fallén 1805), Philaenus spumarius (Linnaeus 1758) and Cercopis vulnerata Illiger were collected around Cambridge, UK. Lepyronia coleoptrata (Linnaeus 1758)were collected in the region of Nanus and near Ljubljana in Slovenia. All belong to the order Hemiptera, suborder Auchenorrhyncha and to the superfamily Cercopoidea. Cercopis belongs to the family Cercopidae, the others to the family Aphrophoridae.

The anatomy of the hind legs and metathorax was examined in live insects,in insects preserved in 50% glycerol, in 70% alcohol, after fixation in 5%buffered formaldehyde and subsequent storage in 70% alcohol, and when cleared by boiling in 5% potassium hydroxide. Drawings of the legs, joints and muscles were made with the aid of a drawing tube attached to a Leica MZ8 or MZ16 stereomicroscope. Photographs from these microscopes were made with Nikon D1 or Nikon DXM1200 digital cameras. Dried specimens were also mounted on specimen holders, sputter coated with gold and then examined in a Philips XL-30 Scanning Electron Microscope.

Sequential images of the movements of hind legs that underlie jumping, or imposed movements of the hind legs, were captured at rates of 500, 1000 or 2000 s^-1 with a high speed camera (Redlake Imaging, San Diego, CA,USA) and associated computer. Movements of a hind leg of a restrained Aphrophora or Cercopis were also recorded by gluing a small disc of reflective tape to a hind femur close to the femoro-tibial joint. A modified single lens reflex camera with a concentric light around the lens was focussed on the disc and the light reflected from it was captured by a photocell in the film plane of the camera(Hedwig, 2000).

The hind legs of different species of froghopper are 1.4-1.6 times longer than the front and middle legs but only 52-66% the length of the body(Burrows, 2006). They have a mass that is only 2% of the total body mass, largely because the main muscles powering a jump and controlling the movements of the trochantera are in the thorax (Burrows, 2007). The tibia of a hind leg is longer than the femur(Fig. 1). For example, in Philaenus it is 1.8±0.07 mm (mean ± s.e.m., N=34) and thus 64% longer than the femur (1.1±0.03 mm). In larger froghoppers this difference is accentuated so that in Cercopisa tibia is 81% longer than a femur and in Aphrophora it is 92%longer. A hind tibia in all species has two outwardly pointing spines and two semi-circular rows of smaller spines on its ventral surface close to the articulation with the tarsus. The two most proximal tarsal joints also have a ventral, semi-circular row of spines. These spines should increase traction as thrust is applied through the tibia and tarsus to the ground at take-off in a jump. The front and middle pairs of legs have no spines and have usually lost contact with the ground before take-off in a jump.

Further prominent differences between the hind and the other legs are in the structure of the coxa and the femur(Fig. 1). A hind, but not a front or middle coxa, has a prominent lateral extension, the lateral and anterior corner of which provides one of its two pivot points with the thorax. A ventral, ovoid protrusion also arises from this lateral region of the hind coxa and is visible from a ventral view when the trochanter is depressed but covered by the femur when the leg is fully levated(Fig. 1). It is not present on the front or middle legs. The medial surfaces of the left and right hind coxae, but not those of the front and middle legs, are closely apposed and at these points of contact each has a field of microtrichia [a dense array of small protuberances (Gorb,2004)] that engage with those of the other coxa.

A hind femur has a protrusion on its dorsal surface that is not present on the front or middle legs (Fig. 2A). As the trochanter levates fully, this protrusion rides over the coxal protrusion and engages with it so that in this cocked position(shown on the right in Fig. 1),the proximal femur is closely apposed to the coxa. The more distal parts of a hind leg, including the femoro-tibial joint, then lie between the thorax and a middle leg.

The coxae of the two hind legs are closely apposed at their medial surfaces, in contrast to those of the front and middle legs that are widely separated, so that the mouthparts are interposed between them. A hind coxa can move about its articulation with the sternal region of the metathorax by some 25° in a plane that allows the whole hind leg to be rotated forwards and downwards, or backwards and upwards, in a plane nearly parallel to the long axis of the body (Fig. 2A). When viewed ventrally (see drawing in Fig. 1, Fig. 3 and scanning electron micrographs in Figs 7, 8, and 9), one pivot of this thoraco-coxal joint is seen to be at the anterior, ventral edge of the lateral coxa and the second at the anterior, medial edge of the coxa. Movements of the trochantin, a sclerite embedded in the flexible cuticle linking the coxa anteriorly with the thorax (Fig. 1) have not been analysed.

The pivots of the coxo-trochanteral joint are, by contrast, dorsal and ventral so that the trochanter is depressed or levated in a horizontal plane through angles of 75-100° (Fig. 2C). The ventral pivot is at the lateral edge of the main part of the coxa and close to the lateral edge of the trochanter, whilst the dorsal pivot is more medial.

The femur is not fused to the trochanter and can rotate about it through some 30° (Fig. 2B). The dorsal and ventral pivots are both lateral so that the plane of movement is similar to that of the trochanter. The tibia can flex or extend through some 170° about the femur, again in much the same plane, and the tarsus can levate and depress through some 45° about the tibia(Fig. 2D,E). Thus the segments distal to the coxa move in the same plane that is determined by the rotation of the coxa about the thorax. Thrust applied by depression of the trochanter will thus be applied in the same plane through all of the more distal joints of a hind leg.

To resolve the detailed movements of the proximal joints of the hind legs during jumping, Aphrophora were fixed ventral surface uppermost in Plasticene™ in such a way that all the legs were free to move. Very rapid and simultaneous movements of both hind legs occasionally occurred spontaneously or could be evoked by gentle tickling hairs on the abdomen with a fine paintbrush. No differences in the form, sequence, or timing of the movements of the two hind legs could be discerned in images of these sequences compared with those in free jumping(Burrows, 2006; Burrows, 2007). The sequence of movements of an individual hind leg could be resolved into the following sequence of actions (Fig. 3).

First, there was a slow levation of the trochanter about the coxa and a smaller decrease in the angle of the femur about the trochanter, accompanied by a flexion of the tibia about the femur. These changes moved the femur anteriorly so that it passed ventral to a lateral protrusion on the coxa, with which it then engaged, and medially so that it was pressed against the lateral edge of the coxa (Fig. 3A,B). This cocking movement of a hind leg lasted some 110 ms in the example shown,but in different attempted jumps by Aphrophora, the mean time taken was 187.3±8.9 ms, range 88-353 ms, median 183 ms, N=45(Burrows, 2007).

Second, the hind legs remained in this cocked position without moving for a period of 2 s in this example, though again this period was variable in different attempted jumps by Aphrophora (mean 2.9±0.16 s, N=160) (Burrows,2007). Compression of the ventral thorax during this period meant that the hind legs moved anteriorly and thus closer to the middle legs,thereby pressing the trochantin against the flexible membrane of the metathorax and against the middle legs (see pairs of horizontal lines in Fig. 3A).

Third, after this long period with no visible movements of the leg joints,both hind legs depressed and extended completely in 1 ms(Fig. 3A,B). The main movement of each hind leg was a rapid depression of the trochanter about the stable coxa, accompanied by a small increase in the trochantero-femoral angle that may have resulted from the centrifugal forces generated by the rapid depression of the coxo-trochanteral joint. The structure of this joint was therefore examined in detail.

The cuticle of the coxa and the trochanter close to their pivots is heavily sclerotised and appears black (Fig. 4A-C). A strip of ventral coxal cuticle extending anteriorly from the ventral pivot is also strengthened and sclerotised(Fig. 4A,C). In the dorsal coxa, two struts run medially and laterally from the dorsal pivot to form a V-shaped internal scaffold (Fig. 5B-E). The ventral and dorsal pivots each consist of a curved medially pointing horn of cuticle extending anteriorly from the trochanter that each engage in an indentation of the coxa(Fig. 4A,C; Fig. 5B-D). As the trochanter depresses about these pivots, its ventral anterior edge moves dorsal to a posterior projection of the coxa until at full depression the medial and anterior edge of the trochanter abuts against the medial and posterior edges of the coxa (Fig. 4A,B; Fig. 5A,C). The tendon of the trochanteral depressor muscle inserts on the thickened and sclerotised medial rim of the trochanter, with the area of sclerotisation wrapping around both the ventral and dorsal surfaces of the trochanter(Fig. 4A-C). In contrast to the extensive area of insertion of the depressor tendon, the trochanteral levator muscles insert on two small lateral protrusions of the trochanter, one dorsal(Fig. 5D) and the other ventral, which are again both sclerotised.

The lever ratios of the trochanteral depressor and levator muscles were determined from individual frames captured at rates of 1000 s^-1 as a hind leg moved naturally, or when forcibly moved over its entire angular range. When viewed ventrally (Figs 1, 4) the line of action of the depressor tendon always appears to have a positive mechanical advantage, even when the joint was in its most levated position. It does not appear to go over the centre of the pivot in this cocked position, and because the pivot is so lateral there would be little room for it to move into such a position within the coxa. Images of the joint movement were also captured from a posterior perspective, enabling both pivots to be seen at the same time(Fig. 6A-C). In the most levated (cocked) position, the insertion of the depressor tendon is medial to the pivot and the line of action of the tendon positive. As the coxo-trochanteral joint depressed the distance between the insertion of the tendon and the line of the pivot increased. Plotting the lever arm of the depressor muscle showed that it was smallest at the most levated position(Fig. 6D). For the first 10° of depression movement the lever arm remained the same, but then increased rapidly to a maximum after some 80° of movement and remained at this value during further depression of the joint. By contrast, the lever arm of the levator tendon was similar over the full range of joint movement. The lever arm of the depressor exceeded that of the levator after 40° of depression.

Scanning electron micrographs of the trochantin, coxa and trochanter revealed three prominent arrays of hairs that would appear to act as proprioceptors signalling the movements of one segment of a hind leg relative to another (Fig. 7). The movements that all three are likely to signal are those that occur in preparation for jumping. Other leg movements that have been observed would not be likely to stimulate them.

First, a hair row on the trochantin consists of some 15 hairs (trichoid sensilla), 15-50 μm long, which are stouter than those distributed more widely over the legs and body (Fig. 7A,B). They would be stimulated when the trochantin either touches the flexible membrane linking it to the mesothorax, or the middle legs. Such a movement occurs during the compression of the thorax when the hind legs are held in their cocked positions in preparation for a jump.

Second, on the anterior, ventral surface of the coxa is an approximately circular hair plate, the coxo-trochantinal hair plate, consisting of some 13 hairs (trichoid sensilla), ranging from 8-15 μm in length(Fig. 7A,C). These hairs could signal contact of the coxa with the trochantin during movements that precede the sudden depression of the trochanter in a jump.

Third, on the lateral edge of the trochanter is a hair plate consisting of two rows of regularly spaced hairs, ranging in length from 5-10 m(Fig. 7D). This hair plate could signal the initial contact of the trochanter with the lateral, distal edge of the coxa when it is levated into its fully cocked position, and the continuing contact while it is held cocked before a jump.

In the fully levated position, the femur of a hind leg moves ventral to the lateral, ventral protrusion of the coxa so that it is closely engaged with it(Figs 1, 3). The detailed structure of this region of engagement was therefore examined in the scanning electron microscope from a ventral perspective for the coxa(Fig. 8A-D) and from a dorsal perspective for the femur (Fig. 9A-D).

Micrographs show clearly that the oval, domed-shaped lateral protrusion is part of the coxa, and that in contrast to the surrounding cuticle of the coxa,it is covered in a dense array of small protrusions called microtrichia(Fig. 8B-D). They are similar in appearance to those on the apposed, medial surfaces of the coxae(Gorb, 2004). Over most of a coxal protrusion the microtrichia are 5-8 μm high, 3-6 μm wide and are separated by intervals of 1-2 μm. The size decreases with distance from the peak of the protrusion and the spacing between them increases so that they taper into the smooth cuticle of the rest of the coxa. The microtrichia on the dome of the protrusion point anteriorly. In many coxae examined in fixed insects, the dome of the protrusion was dimpled and the microtrichia there appeared flattened (Fig. 8C). In live insects, the cuticle on the dome is soft and can easily be dimpled by slight external pressure, indicating that its appearance in the micrographs most likely results from the collapse of the underlying, flexible membrane.

On the dorsal surface of a femur at its proximal end is a prominent protrusion with its highest point at the anterior edge(Fig. 5A,B,F; Fig. 9A,B). It protrudes by 130μm from the dorsal surface of the femur at a point where the dorso-ventral depth of the femur is 220 μm (Fig. 5F). It tapers steeply on its distal side but more gradually toward the proximal end of the femur. This protrusion is again covered in an array of microtrichia which are somewhat shorter at 4-6 μm high, and broader at 5-7 μm wide and more widely spaced at 2-3 μm than those on the coxal protrusion. The size of the microtrichia decreases and their spacing increases with distance from the slope of the protrusion so that they taper into the smooth cuticle of the surrounding femur. On the protrusion, the microtrichia are oriented posteriorly and somewhat medially.

For a hind leg to move into its most levated (cocked) position, the protrusion on the dorsal femur must ride over the coxal protrusion and engage in front of it. This will bring the two surfaces bearing microtrichia into direct contact with each other and the orientation of the microtrichia on these two surfaces should ensure that many will interlock. Furthermore, the flexible dome on the coxal protrusion should allow it to fit snugly into the shape of the femoral protrusion so that the two sets of microtrichia are fully apposed or engaged. The increased surface area provided by the microtrichia,the interlocking between them and the engagement of the femoral protrusion in front of the coxal protrusion together provide an impediment, or an increased area of friction, to the depression of the leg. To allow the femur to be extended in a jump, these two surfaces must disengage and the femoral protrusion must ride over the coxal protrusion. The hind leg could be held in its cocked position by this mechanism and allowed to move suddenly only when sufficient depression force was generated.

The larvae, which live in the protected environment afforded by their secretion of a froth or `cuckoo spit', have a small coxal protrusion that is smooth and entirely devoid of microtrichia(Fig. 10A). The dorsal surface of the proximal part of a hind femur has no protrusion and no microtrichia(Fig. 10B). The larvae do not jump and if they do emerge from their froth, they walk to another feeding site. The femoral and coxal protrusions, and their associated microtrichia,appear only after the final moult. Within a few minutes of emergence from its froth, an adult is able to jump.

The stages in the movement of a hind leg that allow its release from its fully levated position was analysed in froghoppers that had recently died(Fig. 11). In such insects, a hind leg can be forcibly rotated forwards so that the trochanter is fully levated about the coxa and the femur engaged with the coxal protrusion. The leg will then lock into and remain in its cocked position solely because of the mechanical construction of the leg and in the absence of any active muscular contraction. Sometimes the leg will then spontaneously and rapidly depress, or can be induced to do so by applying a backwards force to the femur or the tibia. During a spontaneous movement from the cocked position, the coxo-trochanteral joint depressed and the femur moved backwards to expose the coxal protrusion to view (Fig. 11A). The movement of the hind leg was rapid and was completed in 2 ms even though it was not powered by any muscular contraction. When powered by muscular contractions, the jump movement in equivalent circumstances (when not bearing the weight of the body) is complete in 0.3 ms (see Fig. 12C) (Burrows, 2006a). The rapidity of the movement in a dead insect, suggests that the forced levation stretched tendons and muscle fibres and elastic force was stored in these structures, or in associated deformations of the cuticle, which was then released suddenly to provide the propulsive power.

In a movement triggered by the application of external force to the distal end of the femur, the unlocking of the leg that must occur before a rapid jump movement could be resolved into two steps(Fig. 11B). The first movement was a small depression of the coxo-trochanteral joint that was then followed by the femoral protrusion disengaging from the coxal protrusion. Only then were the femur and the more distal segments of the leg able to move,demonstrating the contribution of the engagement between the femur and the coxa to the cocking of the hind leg, and its subsequent disengagement to the rapid jumping movement.

When froghoppers performed an unrestrained jump, a consistent click could be heard and recorded by a microphone placed at the point of take-off(Fig. 12A). The sound occurred during take-off. When a froghopper was restrained on its back in Plasticene and encouraged by gentle tickling to produce the rapid, simultaneous movements of its hind legs that underlie jumping, they were again accompanied by a click sound (Fig. 12B). In this experimental arrangement, the hind legs made no contact with the substrate or with any other object, so that the sound must have resulted from the rapid movements of the hind legs themselves. When images of the movement were captured at 1000 s^-1, the sound could be correlated to the 1 ms period when the legs moved from their cocked to their fully depressed position. To provide greater time resolution, a disc of reflective tape was fixed to the distal femur enabling changes in the angle between the coxa and femur to be detected (Fig. 12C). Allowing for the conduction of the sound to a microphone 5 mm away, the sound must have occurred just 0.035 ms after the movement started and full depression of the hind leg was completed in 0.3 ms. The sound must therefore result from events at the very start of the rapid depression movement, such as the initial movement of the coxo-trochanteral joint, or the disengagement of microtrichia on the coxal and femoral protrusions.

Rapid and simultaneous movements of the hind legs propel jumping in froghoppers. High speed images of the jumping movements(Burrows, 2006) and the detailed anatomy presented here suggest that the following sequence of movements underlie jumping. First, the hind legs are levated slowly into their cocked positions and the femoral protrusions engage with their respective coxal protrusions. Second, the hind legs remain stationary for seconds in their cocked position, but the thoracic cuticle is deformed and may act as an energy store (Rothschild et al.,1975; Sander,1957). Third, both hind legs move rapidly by a depression of their coxo-trochanteral joints at angular velocities of 75 500 deg. s^-1and an extension of their tibiae about the femora. These movements are completed in less than 1 ms or 100 times faster than the initial cocking movements, while accelerating the load of the body. For a hind leg to move rapidly from its cocked position, the coxal and femoral protrusions must disengage. A prominent click sound is generated by the early events associated with the rapid depression and extension movements.

The differences in the design of the hind legs of froghoppers and their other two pairs of legs appear to relate to this key role in jumping. The hind legs, however, are short relative to the body, ranging from only 52-66% of body length, and relative to the other legs they are only 1.4-1.6 times longer due entirely to a longer tibia (Burrows,2006). This contrasts with the hind legs of locusts and bush crickets, which are much longer relative to body length. The hind legs of froghoppers are also light, with their mass representing only a small (2%)proportion of body mass, contrasting again with locusts where the proportion is 14% (Bennet-Clark, 1975). In froghoppers, the low mass of the hind legs results from the location of the main power producing muscles (the trochanteral depressors) in the thorax. This is the same as in fleas (Bennet-Clark and Lucey, 1967; Rothschild and Schlein, 1975), but contrasts with locusts where the powerproducing extensor tibiae muscles are in the femur.

The specialisations of the hind legs critical for jumping lie in the detailed structure of particular joints, the improved traction provided by the tibio-tarsal and tarsal joints, strategically placed proprioceptors to monitor the large forces, the presence of a mechanism for locking the femur against the coxa when the leg is cocked in readiness for jumping, and in the lever arrangements of the muscles in the thorax that move the trochanter. All of these features are unique to the hind legs and most are not present in the larvae that have restricted lives underground, or above ground in a protective froth.

The sudden and powerful application of thrust by the hind legs requires good traction if the force is to be applied effectively to the ground. If both legs slip then only a very weak jump occurs and if one leg slips the body skews to one side at take-off. Traction is improved by arrays of small spines at the ventral surface of the articulation of the tibia with the tarsus and at the proximal two tarsal joints. The first movement of a hind leg before take-off results in the tarsus being pushed flat to the ground so that the spines engage with the substrate (Burrows,2006). These arrays of spines are not present on the front and middle legs, and nymphs of Philaenus that do not jump lack prominent arrays of spines on the hind tarsi.

Three external proprioceptors would appear to signal critical aspects in the preparation for a jump and the consequences of the very large forces that are generated. It is likely that more internal proprioceptors and campaniform sensilla exist. First, the prominent hair row on a trochantin is likely to signal movements of a coxa and trochantin as they move forwards due to the contractions of the trochanteral depressor muscle. Second, the hair plate on the medial edge of the coxa could provide additional information about the contraction of the trochanteral depressor muscle by signalling contact with the trochantin during preparation for a jump. Third, the hair plate on the lateral trochanter consists of two rows of stout hairs that are stimulated as the trochanter is levated about the coxa. They could therefore signal the levation movement to the fully cocked position, and the maintenance of the trochanter in this position during preparation for jumping. The movements that would stimulate the first two proprioceptors only occur when the leg is fully levated and the trochanteral depressor muscles are contracting without being able to move the leg from its cocked position. Their likely action is therefore limited to jumping. A full levation of the trochanter that stimulates the third proprioceptor is again only likely to occur if the legs are being cocked in readiness for jumping.

In preparation for a jump, the hind legs are moved into their most levated(cocked) position and remain in that position for seconds before they are rapidly depressed and extended in the movement that powers a jump. In this cocked position, the lever arm of a trochanteral depressor muscle is smallest and is exceeded by the lever arm of the levator. The tendon of a trochanteral depressor muscle inserts on the strengthened medial edge of the trochanter some 500 μm from the joint pivot that is toward the lateral edge of the coxa. This arrangement means that even in the cocked position the trochanteral depressor tendon has a positive mechanical advantage and does not go over-centre. During depression, the lever arm of the depressor muscle increases rapidly to reach a maximum after some 80° of movement. After only 40° of movement, it exceeds the lever arm of the levator that changes little throughout the whole range of joint movement.

To move into the cocked position, a sloping protrusion on the dorsal surface of a hind femur must ride over and engage with a lateral and ventral protrusion of a coxa. Once the femoral protrusion is anterior to the coxal protrusion, the hind leg is effectively cocked and poised to extend by a rapid depression of the trochanter and extension of the tibia. The effectiveness of this passive locking device has been demonstrated experimentally in dead froghoppers. Pushing a hind leg into its cocked position results in it locking under the passive forces of the engagement between the coxal and femoral protrusions, and a possible involvement of the coxo-trochanteral joint. If a force is now applied to a hind leg in the same direction as a depression movement, then resistance is encountered. When the applied force is sufficient to overcome this resistance, a hind leg will suddenly and rapidly extend in about 2 ms, indicating that the cocking movement had stored energy either by stretching muscles and tendons or distorting cuticular elements. Images captured at high speed indicate that the rapid movement occurs only when the femoral and coxal protrusions have disengaged.

The coxal and femoral protrusions are both covered by dense arrays of microtrichia. These increase the friction between two apposed surfaces, or those on one surface may interlock with those of the other, much in the manner of `Velcro' fasteners. Microtrichia are often found in insects wherever two apposed surfaces must lock together under particular circumstances. For example, they are found at the articulation of the head with the prothorax in dragonflies and damselflies where they stabilise the head particularly in flight; in some beetles they occur in patches on the thorax and on the wings to lock the wings to the thorax when not flying; in some Lepidoptera on the front and hind wings to ensure that they are locked together during flight(Gorb, 2001). In froghoppers,microtrichia also occur on the medial surfaces of the hind coxa where they have been interpreted to synchronise the coxae in jumping(Gorb, 2001; Gorb, 2004). I have shown that the critical synchrony in movements of the hind leg during jumping is between the rapid movements of the trochantera. The microtrichia on the two coxae are thus more likely to provide a stable base for these rapid movements than to contribute to the synchrony of the propulsive leg movements.

This elaborate locking mechanism between the femur and coxa is not found in other insects that jump by a rapid propulsive extension of their hind legs,but other locks do occur. No similar structure is described in fleas(Bennet-Clark and Lucey, 1967; Rothschild and Schlein, 1975),which jump by depression of the hind trochantera about the coxae, and in locusts, bush crickets and false stick insects, the propulsion comes from an extension of the tibiae about the femora. In froghoppers, a key role for these structures in jumping is emphasised by their occurrence only on the hind legs of adults. They are not present on the middle and front legs of adults, and in nymphs that do not jump they are also absent on the hind legs. A meracantha on the hind coxa engaging with a yellow spot on the proximal femur has been described on a hind leg of some Homopterans including froghoppers(Emeljanov, 1987) and a protrusion from the coxa has also been described on the hind legs of Lantern Flies (Homoptera, Fulgoridae) (Sander,1957). Emeljanov suggests that these structures could act as a possible proprioceptor but provides no evidence. The meracantha may be the structure to which I have applied the purely descriptive term of coxal protrusion. I have not seen a yellow spot on the femur but perhaps it corresponds to the structure I have called the femoral protrusion. My experiments described here show that these structures provide a locking mechanism, but their engagement could also stimulate nearby hairs or other as yet undescribed sensory structures that could provide further proprioceptive information.

Further understanding of the mechanisms underlying the movements of the hind legs in jumping, requires that timings and sequences of the muscle actions be determined. This will be the subject of my next paper(Burrows, 2007).

I thank my Cambridge colleagues for their many helpful suggestions during the course of this work and for their comments on the manuscript. I am also most grateful to Bill Lee for his expert help with the scanning electron microscopy, and to Steve Rogers and Roger Northfield who helped me catch these insects. I am also most grateful to Dr Meta Virant and her colleagues for all their help and hospitality at the Department of Entomology, National Institute of Biology, Vecna pot 111, P.O.B. 14, SI-1001 Ljubljana, Slovenia, where some of these experiments were performed.