Insect-scale jumping robots enabled by a dynamic buckling cascade.

Millions of years of evolution have allowed animals to develop unusual locomotion capabilities. A striking example is the legless-jumping of click beetles and trap-jaw ants, which jump more than 10 times their body length. Their delicate musculoskeletal system amplifies their muscles' power. It is challenging to engineer insect-scale jumpers that use onboard actuators for both elastic energy storage and power amplification. Typical jumpers require a combination of at least two actuator mechanisms for elastic energy storage and jump triggering, leading to complex designs having many parts. Here, we report the new concept of dynamic buckling cascading, in which a single unidirectional actuation stroke drives an elastic beam through a sequence of energy-storing buckling modes automatically followed by spontaneous impulsive snapping at a critical triggering threshold. Integrating this cascade in a robot enables jumping with unidirectional muscles and power amplification (JUMPA). These JUMPA systems use a single lightweight mechanism for energy storage and release with a mass of 1.6 g and 2 cm length and jump up to 0.9 m, 40 times their body length. They jump repeatedly by reengaging the latch and using coiled artificial muscles to restore elastic energy. The robots reach their performance limits guided by theoretical analysis of snap-through and momentum exchange during ground collision. These jumpers reach the energy densities typical of the best macroscale jumping robots, while also matching the rapid escape times of jumping insects, thus demonstrating the path toward future applications including proximity sensing, inspection, and search and rescue.

Nonlinear elasticity and damping govern ultrafast dynamics in click beetles.

Many small animals use springs and latches to overcome the mechanical power output limitations of their muscles. Click beetles use springs and latches to bend their bodies at the thoracic hinge and then unbend extremely quickly, resulting in a clicking motion. When unconstrained, this quick clicking motion results in a jump. While the jumping motion has been studied in depth, the physical mechanisms enabling fast unbending have not. Here, we first identify and quantify the phases of the clicking motion: latching, loading, and energy release. We detail the motion kinematics and investigate the governing dynamics (forces) of the energy release. We use high-speed synchrotron X-ray imaging to observe and analyze the motion of the hinge's internal structures of four Elater abruptus specimens. We show evidence that soft cuticle in the hinge contributes to the spring mechanism through rapid recoil. Using spectral analysis and nonlinear system identification, we determine the equation of motion and model the beetle as a nonlinear single-degree-of-freedom oscillator. Quadratic damping and snap-through buckling are identified to be the dominant damping and elastic forces, respectively, driving the angular position during the energy release phase. The methods used in this study provide experimental and analytical guidelines for the analysis of extreme motion, starting from motion observation to identifying the forces causing the movement. The tools demonstrated here can be applied to other organisms to enhance our understanding of the energy storage and release strategies small animals use to achieve extreme accelerations repeatedly.

Latching of the click beetle (Coleoptera: Elateridae) thoracic hinge enabled by the morphology and mechanics of conformal structures.

Elaterid beetles have evolved to 'click' their bodies in a unique maneuver. When this maneuver is initiated from a stationary position on a solid substrate, it results in a jump not carried out by the traditional means of jointed appendages (i.e. legs). Elaterid beetles belong to a group of organisms that amplify muscle power through morphology to produce extremely fast movements. Elaterids achieve power amplifications through a hinge situated in the thoracic region. The actuating components of the hinge are a peg and mesosternal lip, two conformal parts that latch to keep the body in a brace position until their release, the 'click', that is the fast launch maneuver. Although prior studies have identified this mechanism, they were focused on the ballistics of the launched body or limited to a single species. In this work, we identify specific morphological details of the hinges of four click beetle species - Alaus oculatus, Parallelostethus attenuatus, Lacon discoideus and Melanotus spp. - which vary in overall length from 11.3 to 38.8 mm. Measurements from environmental scanning electron microscopy (ESEM) and computerized tomography (CT) were combined to provide comparative structural information on both exterior and interior features of the peg and mesosternal lip. Specifically, ESEM and CT reveal the morphology of the peg, which is modeled as an Euler-Bernoulli beam. In the model, the externally applied force is estimated using a micromechanical experiment. The equivalent stiffness, defined as the ratio between the applied force and the peg tip deflection, is estimated for all four species. The estimated peg tip deformation indicates that, under the applied forces, the peg is able to maintain the braced position of the hinge. This work comprehensively describes the critical function of the hinge anatomy through an integration of specific anatomical architecture and engineering mechanics for the first time.