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Meadow froghopper (Philaenus spumarius) by Charles J Sharp is licensed under CC BY-SA 4.0
Grasshoppers are not the only animals that use catapults to beat the power limitations of muscle. Here is a selection of other examples:
Different people snap their fingers in slightly different ways, but we all use the same basic mechanism. This is the way I do it. First I press the tip of my second finger against the tip of my thumb. This is like the grasshopper flexing its back legs. Next I contract the forearm muscles which pull my finger towards my wrist. However, the finger doesn't move because it's locked against the thumb. The contraction is quite slow and powerful, and the tendons of the muscle stretch slightly, storing energy. Finally, the finger slips off the tip of the thumb, and snaps against the base of the thumb. The movement is powered mainly by the energy stored in the tendons.
There is a nice video of this (not me!) on Wikipedia.
Try snapping your finger without first locking it against the thumb. You can't produce a satisfying snap using direct muscle power alone!
Froghoppers are sap-sucking insects whose larvae are responsible for the famous "cuckoo spit" often seen on leaves in the garden. The adults are only about 6 mm long, but they can jump as high as 0.7 m - more than 100 times their body length. Because of their very short legs, they require an acceleration of about 5,400 m s-2, which is more than 500 times that of gravity. This is one of the fastest accelerations known in any animal.
These animals jump by extending their legs from the "hip" (trochanter), rather than the knee like a grasshopper. Before they jump they fold up their legs against their "chest" (thorax), and lock them into place using something similar in principle to Velcro pads but very much smaller - the hairs on the pads (microtrichia) are only a few microns long. The main jumping muscles then contract, and store energy in internal springs within the thorax. When the force reaches a high enough level the Velcro pads simply rip apart and the legs thrust downwards.
So froghopper jumping is a 3-stage process just like the grasshopper, but unlike the grasshopper there is no need for an antagonist muscle to hold the legs in the pre-jump position, and there is no positive neural control of the timing of release. Instead, the lock and release are achieved by purely mechanical effects. This is a classic case of convergent evolution - the problem of making a rapid movement is solved by using a mechanical spring for power amplification in both animals, but the details of the solution are very different and have evolved independently from each other.
Meadow froghopper (Philaenus spumarius) by Charles J Sharp is licensed under CC BY-SA 4.0
Fleas are good jumpers, but have very small legs. The acceleration they need to get to their take-off velocity can be more than 3000 m.s-2 (i.e. about 320 gravities), so it will come as no surprise that they too use a catapult mechanism. An interesting question is, where's the elastic?
Fleas are wingless insects, but this is a quite recent (in geological terms) adaptation to parasitism. Fleas evolved from insect ancesters that did have wings. All insect wings pivot on a special hinge mechanism, made from very elastic cuticle (called resilin). The hinge saves energy for a flying insect by helping the wings to "bounce" up and down. Fleas have lost their wings, but kept their wing hinges! The structure which used to be the wing hinge is now a chunk of rubbery cuticle in the side of the body, and this is the elastic spring which gets compressed to store the energy for the jump.
On the left (or on top) is a flea (Oropsylla montana - one of the vectors of the plague bacillus in the US) by Kat Masback, licenced under CC BY-SA 2.0. On the right is the ghost of a flea by William Blake (c1819-20), public domain via Wikimedia Commons.
The mantid shrimps ("thumb-splitters") have large claws (actually modified mouthparts) which they can fling out extremely rapidly, spearing or clubbing their prey with the power of a small-calibre bullet. They use a process very similar to that of the grasshopper, in which the claw is locked into the pre-strike position using a relatively weak muscle. This muscle continues to contract, holding the claw locked, while the main muscle builds up force slowly. Finally, the weak muscle relaxes, the limb shoots out, and the rest is history (or the prey is toast).
Perhaps surprisingly, the more famous Praying Mantis, which is an insect, does not seem to use a catapult mechanism. It flings out its front legs to catch its prey, but the movement is not actually all that fast, and is apparently driven by direct muscle action.
Springtails (Collembola) are genuinely flightless insects that have a special lever under their abdomens. This gets locked in a flexed position using a cuticular catch, and then extends rapidly to flick the animal into the air. Click beetles (Coleoptera) lie on their backs and lock their bodies into an arched position. They then contract their ventral muscles until the lock gives way. The head and the tail thus rapidly flex together, flinging the whole body into the air.
Trap-jaw ants (Hymenoptera) have enlarged jaws which they can lock open. They then slowly contract the closer muscles to store energy, and at the last moment contract a small jaw muscle which undoes the lock. The jaws spring shut on the prey.
Pistol shrimps ("the fastest claw in the west") lock their claws in an open position using two extremely flat cuticle plates, that come together in the open position and stick due to surface tension. The closer muscle contracts slowly, and the claws shut rapidly when the force overcomes the "sticktion". Apparently, tired pistol shrimps get their claws stuck in the open position, and can't close them until their muscles have recovered.
One of the few examples of jumping in soft-bodied animals is found in the larva of the Mediterranean fruit fly. Hooks near the mouth anchor the head to the ground, and then the body is arched to bring the tail up to the head. Body muscles then tense and the hooks unlatch, flinging the animal upwards and forwards a distance of about 10 cms.
Finally, it seems worth mentioning the leaf-rolling caterpillars (Lepidoptera) with the charming habit of firing faecal pellets from their anuses. A structure called the anal plate is loaded with a faecal pellet, and then retracted into the pre-firing position and held in place by a cuticular catch. The blood pressure in the anal compartment is then raised by contracting nearby muscles. When the pressure reaches a sufficient level, the catch gives way and the anal plate flicks the pellet out at a velocity of over 1 m.s-1!
You have now finished reading about how grasshoppers jump. All that's left is the bibliography, which tells you where you can find the original research papers describing what I have been talking about.