A physical model of mantis shrimp for exploring the dynamics of ultrafast systems

Design and control of jumping microrobots with torque reversal latches

Jumping microrobots and insects power their impressive leaps through systems of springs and latches. Using springs and latches, rather than motors or muscles, as actuators to power jumps imposes new challenges on controlling the performance of the jump. In this paper, we show how tuning the motor and spring relative to one another in a torque reversal latch can lead to an ability to control jump output, producing either tuneable (variable) or stereotyped jumps. We develop and utilize a simple mathematical model to explore the underlying design, dynamics, and control of a torque reversal mechanism, provides the opportunity to achieve different outcomes through the interaction between geometry, spring properties, and motor voltage. We relate system design and control parameters to performance to guide the design of torque reversal mechanisms for either variable or stereotyped jump performance. We then build a small (356 mg) microrobot and characterize the constituent components (e.g. motor and spring). Through tuning the actuator and spring relative to the geometry of the torque reversal mechanism, we demonstrate that we can achieve jumping microrobots that both jump with different take-off velocities given the actuator input (variable jumping), and those that jump with nearly the same take-off velocity with actuator input (stereotyped jumping). The coupling between spring characteristics and geometry in this system has benefits for resource-limited microrobots, and our work highlights design combinations that have synergistic impacts on output, compared to others that constrain it. This work will guide new design principles for enabling control in resource-limited jumping microrobots.

Bio-inspired apparatus to produce luminescent cavitation in a rigid walled chamber

A mechanical device inspired by the rapid rotational motion of the pistol shrimp plunger has been developed to experimentally study the contraction/expansion dynamics of a gas bubble inside a confined liquid volume and in the vicinity of solid surfaces. The apparatus consists of a limb with a V-shaped end, which fits into a socket forming a cylindrical compression chamber. Air bubbles of different sizes and in different positions inside the chamber were seeded to study their shape evolution in liquids when subjected to pressure pulses induced by the limb closure. By changing the standoff and curvature parameters, as well as the closing power of the limb it was possible to control the dynamical behavior of the cavity. Four stages describing the dynamic behavior of the bubble were found: 1) A slight expansion-contraction stage accompanied by very weak volumetric oscillations. 2) First compression stage. The formation of gas and liquid micro-jets is observed when the vertical symmetry axis of the bubble is initially located outside of the chamber symmetry axis, on the other hand, when there is a coincidence between these axes, the bubble only contracts exhibiting non-spherical shapes, alternating between oblate and prolate spheroidal structures. 3) An expansion stage where the cavity reaches the walls of the chamber exhibiting irregular shapes on its surface. 4) Second compression stage. This process begins when the limb rebounds and stops sealing the chamber allowing a jet of liquid to enter from the fluid medium outside, inducing a very violent collapse accompanied by the emission of light. The proposed technique represents a novel alternative to study the dynamic evolution of bubbles near and on solid boundaries of various geometries. Other attractive features of the apparatus are its low manufacturing cost, simple design and compact size which makes it easily portable.

The effects of temperature on elastic energy storage and release in a system with a dynamic mechanical advantage latch

Changes in temperature alter muscle kinetics and in turn affect whole-organism performance. Some organisms use the elastic recoil of biological springs, structures which are far less temperature sensitive, to power thermally robust movements. For jumping frogs, the use of elastic energy in tendons is facilitated through a geometric latching mechanism that operates through dynamic changes in the mechanical advantage (MA) of the hindlimb. Despite the well-documented use of elastic energy storage, frog jumping is a locomotor behavior that is significantly affected by changes in temperature. Here, we used an in vitro muscle preparation interacting in real time with an in silico model of a legged jumper to understand how changes in temperature affect the flow of energy in a system using a MA latch. We used the plantaris longus muscle-tendon unit (MTU) to power a virtual limb with changing MA and a mass being accelerated through a real-time feedback controller. We quantified the amount of energy stored in and recovered from elastic structures and the additional contribution of direct muscle work after unlatching. We found that temperature altered the duration of the energy loading and recovery phase of the in vitro/in silico experiments. We found that the early phase of loading was insensitive to changes in temperature. However, an increase in temperature did increase the rate of force development, which in turn allowed for increased energy storage in the second phase of loading. We also found that the contribution of direct muscle work after unlatching was substantial and increased significantly with temperature. Our results show that the thermal robustness achieved by an elastic mechanism depends strongly on the nature of the latch that mediates energy flow, and that the relative contribution of elastic and direct muscle energy likely shapes the thermal sensitivity of locomotor systems.

Controlling jumps through latches in small jumping robots

Small jumping robots can use springs to maximize jump performance, but they are typically not able to control the height of each jump owing to design constraints. This study explores the use of the jumper's latch, the component that mediates the release of energy stored in the spring, as a tool for controlling jumps. A reduced-order model that considers the dynamics of the actuator pulling the latch and the effect of spring force on the latch is presented. This model is then validated using high speed video and ground reaction force measurements from a 4gjumper. Both the model and experimental results demonstrate that jump performance in small insect-inspired resource-constrained robots can be tuned to a range of outputs using latch mediation, despite starting with a fixed spring potential energy. For a fixed set of input voltages to the latch actuator, the results also show that a jumper with a larger latch radius has greater tunability. However, this greater tunability comes with a trade-off in maximum performance. Finally, we define a new metric, 'Tunability Range,' to capture the range of controllable jump behaviors that a jumper with a fixed spring compression can attain given a set of control inputs (i.e. latch actuation voltage) to choose from.

Development of an impulsive motion generator inspired by cocking slip joint of snapping shrimp

We propose an impulsive motion generator inspired by snapping shrimp. The proposed device mimics the geometrical arrangement of a unique claw joint calledcocking slip jointand integrates it with an artificial rack-pinion actuator mechanism rather than adopting the musculoskeletal system as it is. The design approach allows the proposed device to reproduce the impulsive slip motion through the torque reversal and unlatching mechanism of the underlying unique joint by using a single servo motor. Static and dynamic analyses revealed that the actuator force required to store and release elastic energy was remarkably small compared with the resulting acceleration force and rotation/tip speed. Through simulations and experiments, we validated the mechanical analyses and confirmed that the resulting ultrafast slip motion was comparable with the claw closure of snapping shrimp based on the cocking slip joint. Moreover, from an engineering perspective, the motion profiles are modifiable through design parameters, and the repeatability of the impulsive slip motion is satisfactory.

Designing continuous equilibrium structures that counteract gravity in any orientation

This paper presents a framework that can transform reconfigurable structures into systems with continuous equilibrium. The method involves adding optimized springs that counteract gravity to achieve a system with a nearly flat potential energy curve. The resulting structures can move or reconfigure effortlessly through their kinematic paths and remain stable in all configurations. Remarkably, our framework can design systems that maintain continuous equilibrium during reorientation, so that a system maintains a nearly flat potential energy curve even when it is rotated with respect to a global reference frame. This ability to reorient while maintaining continuous equilibrium greatly enhances the versatility of deployable and reconfigurable structures by ensuring they remain efficient and stable for use in different scenarios. We apply our framework to several planar four-bar linkages and explore how spring placement, spring types, and system kinematics affect the optimized potential energy curves. Next, we show the generality of our method with more complex linkage systems that carry external masses and with a three-dimensional origami-inspired deployable structure. Finally, we adopt a traditional structural engineering approach to give insight on practical issues related to the stiffness, reduced actuation forces, and locking of continuous equilibrium systems. Physical prototypes support the computational results and demonstrate the effectiveness of our method. The framework introduced in this work enables the stable, and efficient actuation of reconfigurable structures under gravity, regardless of their global orientation. These principles have the potential to revolutionize the design of robotic limbs, retractable roofs, furniture, consumer products, vehicle systems, and more.

A power amplification dyad in seahorses

Throughout evolution, organisms repeatedly developed elastic elements to power explosive body motions, overcoming ubiquitous limits on the power capacity of fast-contracting muscles. Seahorses evolved such a latch-mediated spring-actuated (LaMSA) mechanism; however, it is unclear how this mechanism powers the two complementary functions necessary for feeding: rapidly swinging the head towards the prey, and sucking water into the mouth to entrain it. Here, we combine flow visualization and hydrodynamic modelling to estimate the net power required for accelerating the suction feeding flows in 13 fish species. We show that the mass-specific power of suction feeding in seahorses is approximately three times higher than the maximum recorded from any vertebrate muscle, resulting in suction flows that are approximately eight times faster than similar-sized fishes. Using material testing, we reveal that the rapid contraction of the sternohyoideus tendons can release approximately 72% of the power needed to accelerate the water into the mouth. We conclude that the LaMSA system in seahorses is powered by two elastic elements, the sternohyoideus and epaxial tendons. These elements jointly actuate the coordinated acceleration of the head and the fluid in front of the mouth. These findings extend the known function, capacity and design of LaMSA systems.

Adapting small jumping robots to compliant environments

Jumping animals launch themselves from surfaces that vary widely in compliance from grasses and shrubs to tree branches. However, studies of robotic jumpers have been largely limited to those jumping from rigid substrates. In this paper, we leverage recent work describing how latches in jumping systems can mediate the transition from stored potential energy to kinetic energy. By including a description of the latch in our system model of both the jumper and compliant substrate, we can describe conditions in which a jumper can either lose energy to the substrate or recover energy from the substrate resulting in an improved jump performance. Using our mathematical model, we illustrate how the latch plays a role in the ability of a system to adapt its jump performance to a wide range of substrates that vary in their compliance. Our modelling results are validated using a 4 g jumper with a range of latch designs jumping from substrates with varying mass and compliance. Finally, we demonstrate the jumper recovering energy from a tree branch during take-off, extending these mechanistic findings to robots interacting with a more natural environment.

Developing elastic mechanisms: ultrafast motion and cavitation emerge at the millimeter scale in juvenile snapping shrimp

Organisms such as jumping froghopper insects and punching mantis shrimp use spring-based propulsion to achieve fast motion. Studies of elastic mechanisms have primarily focused on fully developed and functional mechanisms in adult organisms. However, the ontogeny and development of these mechanisms can provide important insights into the lower size limits of spring-based propulsion, the ecological or behavioral relevance of ultrafast movement, and the scaling of ultrafast movement. Here, we examined the development of the spring-latch mechanism in the bigclaw snapping shrimp, Alpheus heterochaelis (Alpheidae). Adult snapping shrimp use an enlarged claw to produce high-speed strikes that generate cavitation bubbles. However, until now, it was unclear when the elastic mechanism emerges during development and whether juvenile snapping shrimp can generate cavitation at this size. We reared A. heterochaelis from eggs, through their larval and postlarval stages. Starting 1 month after hatching, the snapping shrimp snapping claw gradually developed a spring-actuated mechanism and began snapping. We used high-speed videography (300,000 frames s-1) to measure juvenile snaps. We discovered that juvenile snapping shrimp generate the highest recorded accelerations (5.8×105±3.3×105 m s-2) for repeated-use, underwater motion and are capable of producing cavitation at the millimeter scale. The angular velocity of snaps did not change as juveniles grew; however, juvenile snapping shrimp with larger claws produced faster linear speeds and generated larger, longer-lasting cavitation bubbles. These findings establish the development of the elastic mechanism and cavitation in snapping shrimp and provide insights into early life-history transitions in spring-actuated mechanisms.

Geometric latches enable tuning of ultrafast, spring-propelled movements

The smallest, fastest, repeated-use movements are propelled by power-dense elastic mechanisms, yet the key to their energetic control may be found in the latch-like mechanisms that mediate transformation from elastic potential energy to kinetic energy. Here, we tested how geometric latches enable consistent or variable outputs in ultrafast, spring-propelled systems. We constructed a reduced-order mathematical model of a spring-propelled system that uses a torque reversal (over-center) geometric latch. The model was parameterized to match the scales and mechanisms of ultrafast systems, specifically snapping shrimp. We simulated geometric and energetic configurations that enabled or reduced variation of strike durations and dactyl rotations given variation of stored elastic energy and latch mediation. Then, we collected an experimental dataset of the energy storage mechanism and ultrafast snaps of live snapping shrimp (Alpheus heterochaelis) and compared our simulations with their configuration. We discovered that snapping shrimp deform the propodus exoskeleton prior to the strike, which may contribute to elastic energy storage. Regardless of the amount of variation in spring loading duration, strike durations were far less variable than spring loading durations. When we simulated this species' morphological configuration in our mathematical model, we found that the low variability of strike duration is consistent with their torque reversal geometry. Even so, our simulations indicate that torque reversal systems can achieve either variable or invariant outputs through small adjustments to geometry. Our combined experiments and mathematical simulations reveal the capacity of geometric latches to enable, reduce or enhance variation of ultrafast movements in biological and synthetic systems.

Spring and latch dynamics can act as control pathways in ultrafast systems

Ultrafast movements propelled by springs and released by latches are thought limited to energetic adjustments prior to movement, and seemingly cannot adjust once movement begins. Even so, across the tree of life, ultrafast organisms navigate dynamic environments and generate a range of movements, suggesting unrecognized capabilities for control. We develop a framework of control pathways leveraging the non-linear dynamics of spring-propelled, latch-released systems. We analytically model spring dynamics and develop reduced-parameter models of latch dynamics to quantify how they can be tuned internally or through changing external environments. Using Lagrangian mechanics, we test feedforward and feedback control implementation via spring and latch dynamics. We establish through empirically-informed modeling that ultrafast movement can be controllably varied during latch release and spring propulsion. A deeper understanding of the interconnection between multiple control pathways, and the tunability of each control pathway, in ultrafast biomechanical systems presented here has the potential to expand the capabilities of synthetic ultra-fast systems and provides a new framework to understand the behaviors of fast organisms subject to perturbations and environmental non-idealities.

Magnetically actuated gearbox for the wireless control of millimeter-scale robots

The limited force or torque outputs of miniature magnetic actuators constrain the locomotion performances and functionalities of magnetic millimeter-scale robots. Here, we present a magnetically actuated gearbox with a maximum size of 3 millimeters for driving wireless millirobots. The gearbox is assembled using microgears that have reference diameters down to 270 micrometers and are made of aluminum-filled epoxy resins through casting. With a magnetic disk attached to the input shaft, the gearbox can be driven by a rotating external magnetic field, which is not more than 6.8 millitesla, to produce torque of up to 0.182 millinewton meters at 40 hertz. The corresponding torque and power densities are 12.15 micronewton meters per cubic millimeter and 8.93 microwatt per cubic millimeter, respectively. The transmission efficiency of the gearbox in the air is between 25.1 and 29.2% at actuation frequencies ranging from 1 to 40 hertz, and it lowers when the gearbox is actuated in viscous liquids. This miniature gearbox can be accessed wirelessly and integrated with various functional modules to repeatedly generate large actuation forces, strains, and speeds; store energy in elastic components; and lock up mechanical linkages. These characteristics enable us to achieve a peristaltic robot that can crawl on a flat substrate or inside a tube, a jumping robot with a tunable jumping height, a clamping robot that can sample solid objects by grasping, a needle-puncture robot that can take samples from the inside of the target, and a syringe robot that can collect or release liquids.

Dual spring force couples yield multifunctionality and ultrafast, precision rotation in tiny biomechanical systems

Small organisms use propulsive springs rather than muscles to repeatedly actuate high acceleration movements, even when constrained to tiny displacements and limited by inertial forces. Through integration of a large kinematic dataset, measurements of elastic recoil, energetic math modeling and dynamic math modeling, we tested how trap-jaw ants (Odontomachus brunneus) utilize multiple elastic structures to develop ultrafast and precise mandible rotations at small scales. We found that O. brunneus develops torque on each mandible using an intriguing configuration of two springs: their elastic head capsule recoils to push and the recoiling muscle-apodeme unit tugs on each mandible. Mandibles achieved precise, planar, circular trajectories up to 49,100 rad s-1 (470,000 rpm) when powered by spring propulsion. Once spring propulsion ended, the mandibles moved with unconstrained and oscillatory rotation. We term this mechanism a 'dual spring force couple', meaning that two springs deliver energy at two locations to develop torque. Dynamic modeling revealed that dual spring force couples reduce the need for joint constraints and thereby reduce dissipative joint losses, which is essential to the repeated use of ultrafast, small systems. Dual spring force couples enable multifunctionality: trap-jaw ants use the same mechanical system to produce ultrafast, planar strikes driven by propulsive springs and for generating slow, multi-degrees of freedom mandible manipulations using muscles, rather than springs, to directly actuate the movement. Dual spring force couples are found in other systems and are likely widespread in biology. These principles can be incorporated into microrobotics to improve multifunctionality, precision and longevity of ultrafast systems.