Flightless animals have evolved diverse mechanisms to control their movements in air, whether falling with gravity or propelling against it. Many insects jump as a primary mode of locomotion and must therefore precisely control the large torques generated during takeoff. For example, to minimize spin (angular momentum of the body) at takeoff, plant-sucking bugs apply large equal and opposite torques from two propulsive legs [1]. Interacting gear wheels have evolved in some to give precise synchronization of these legs [2, 3]. Once airborne, as a result of either jumping or falling, further adjustments may be needed to control trajectory and orient the body for landing. Tails are used by geckos to control pitch [4, 5] and by Anolis lizards to alter direction [6, 7]. When falling, cats rotate their body [8], while aphids [9] and ants [10, 11] manipulate wind resistance against their legs and thorax. Falling is always downward, but targeted jumping must achieve many possible desired trajectories. We show that when making targeted jumps, juvenile wingless mantises first rotated their abdomen about the thorax to adjust the center of mass and thus regulate spin at takeoff. Once airborne, they then smoothly and sequentially transferred angular momentum in four stages between the jointed abdomen, the two raptorial front legs, and the two propulsive hind legs to produce a controlled jump with a precise landing. Experimentally impairing abdominal movements reduced the overall rotation so that the mantis either failed to grasp the target or crashed into it head first.

Lacewings launch themselves into the air by simultaneous propulsive movements of the middle and hind legs as revealed in video images captured at a rate of 1000 s −1 . These movements were powered largely by thoracic trochanteral depressor muscles but did not start from a particular preset position of these legs. Ridges on the lateral sides of the meso-and metathorax fluoresced bright blue when illuminated with ultraviolet light, suggesting the presence of the elastic protein resilin. The middle and hind legs were longer than the front legs but their femora and tibiae were narrow tubes of similar diameter. Jumps were of two types. First, those in which the body was oriented almost parallel to the ground (−7±8 deg in green lacewings, 13.7±7 deg in brown lacewings) at take-off and remained stable once animals were airborne. The wings did not move until 5 ms after take-off when flapping flight ensued. Second, were jumps in which the head pointed downwards at take-off (green lacewings, −37±3 deg; brown lacewings, −35±4 deg) and the body rotated in the pitch plane once airborne without the wings opening. The larger green lacewings (mass 9 mg, body length 10.3 mm) took 15 ms and the smaller brown lacewings (3.6 mg and 5.3 mm) 9 ms to accelerate the body to mean take-off velocities of 0.6 and 0.5 m s −1. During their fastest jumps green and brown lacewings experienced accelerations of 5.5 or 6.3 g, respectively. They required an energy expenditure of 5.6 or 0.7 μJ, a power output of 0.3 or 0.1 mW and exerted a force of 0.6 or 0.2 mN. The required power was well within the maximum active contractile limit of normal muscle, so that jumping could be produced by direct muscle contractions without a power amplification mechanism or an energy store.

To test whether jumping launches moths into the air, take-off by 58 species, ranging in mass from 0.1 to 220 mg, was captured in videos at 1000 frames s −1. Three strategies for jumping were identified. First, rapid movements of both middle and hind legs provided propulsion while the wings remained closed. Second, middle and hind legs again provided propulsion but the wings now opened and flapped after takeoff. Third, wing and leg movements both began before take-off and led to an earlier transition to powered flight. The middle and hind legs were of similar lengths and were between 10 and 130% longer than the front legs. The rapid depression of the trochantera and extension of the middle tibiae began some 3 ms before similar movements of the hind legs, but their tarsi lost contact with the ground before takeoff. Acceleration times ranged from 10 ms in the lightest moths to 25 ms in the heaviest ones. Peak take-off velocities varied from 0.6 to 0.9 m s −1 in all moths, with the fastest jump achieving a velocity of 1.2 m s −1 . The energy required to generate the fastest jumps was 1.1 µJ in lighter moths but rose to 62.1 µJ in heavier ones. Mean accelerations ranged from 26 to 90 m s −2 and a maximum force of 9 g was experienced. The highest power output was within the capability of normal muscle so that jumps were powered by direct contractions of muscles without catapult mechanisms or energy storage.

High-speed video analyses of the natural behaviour of parasitoid wasps revealed three strategies used to launch the insects into the air. Which strategy is the most energy efficient? In , 92% of take-offs by were propelled entirely by movements of the middle and hind legs, which were depressed at their coxo-trochanteral and extended at their femoro-tibial joints. The front legs left the ground first, followed by the hind legs, so that the middle legs provided the final propulsion. Second, in other species of a similar mass, and , all take-offs were propelled by a mean of 2.8 and 3.8 wingbeats, respectively, with little or no contribution from the legs. The first strategy resulted in take-off times that were four times shorter (5 versus 22.8 ms) and take-off velocities that were four times faster (0.8 versus 0.2 m s). Calculations from the kinematics indicate that propulsion by the legs was the most energy-efficient strategy, because more energy is put into propulsion of the body, whereas in take-off propelled by repetitive wing movements energy is lost to generating these movements and moving the air. In heavier species such as and, take-off was propelled by the combined movements of the middle and hind legs and wingbeats. In , this resulted in the longest mean take-off time of 33.8 ms but an intermediate take-off velocity of 0.4 m s In all three strategies the performance could be explained without invoking energy storage and power amplification mechanisms.

Analysis of the kinematics of take-off in the planthopper Proutista moesta (Hemiptera, Fulgoroidea, family Derbidae) from high-speed videos showed that these insects used two distinct mechanisms involving different appendages. The first was a fast take-off (55.7% of 106 take-offs by 11 insects) propelled by a synchronised movement of the two hind legs and without participation of the wings. The body was accelerated in 1 ms or less to a mean take-off velocity of 1.7 m s −1 while experiencing average forces of more than 150 times gravity. The power required from the leg muscles implicated a poweramplification mechanism. Such take-offs propelled the insect along its trajectory a mean distance of 7.9 mm in the first 5 ms after take-off. The second and slower take-off mechanism (44.3% of take-offs) was powered by beating movements of the wings alone, with no discernible contribution from the hind legs. The resulting mean acceleration time was 16 times slower at 17.3 ms, the mean final velocity was six times lower at 0.27 m s −1 , the g forces experienced were 80 times lower and the distance moved in 5 ms after take-off was 7 times shorter. The power requirements could be readily met by direct muscle contraction. The results suggest a testable hypothesis that the two mechanisms serve distinct behavioural actions: the fast take-offs could enable escape from predators and the slow take-offs that exert much lower ground reaction forces could enable take-off from more flexible substrates while also displacing the insect in a slower and more controllable trajectory.Comparison of take-off performance using two mechanisms: (1) fast take-off propelled by hind legs and (2) slow take-off propelled by wings. Data in columns 2-6 are the grand means (±s.e.m.) for the measured jumping performance of all insects analysed. The values in columns 7-12 are calculated from these means. N=number of individuals performing this type of take-off. The best performance is based on the take-off with the highest velocity. 6