How Hummingbird Beaks Inspire Future Micro Machine Design

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17 Aug 2023

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Have you ever wondered how hummingbirds can open and close their beaks so quickly and precisely? Or how proteins can perform various functions by changing their shapes in response to small stimuli?
These are examples of natural systems that operate around a mathematical concept called a bifurcation, which allows them to switch between different stable states with minimal energy input.

Now, imagine if we could design artificial machines that can do the same thing at the microscale, i.e., the scale of millionths of a meter. Such machines could have many applications in fields like biotechnology, medicine, robotics, and computing. For instance, they could be used to create sensors, actuators, switches, logic gates, memory devices, and more.

This is the goal of a Cornell research team led by Itai Cohen, professor of physics in the College of Arts and Sciences. They have developed a new way to design complex microscale machines, one that draws inspiration from the operation of proteins and hummingbird beaks. Their paper, “Bifurcation Instructed Design of Multistate Machines,” was published in Proceedings of the National Academy of Sciences.

What is a Bifurcation?

A bifurcation is a point where a system undergoes a sudden change in its behavior or structure as a result of a small change in a parameter. For example, consider a ball rolling on a curved surface. Depending on the height and shape of the surface, the ball can have one or two stable positions: either at the bottom or at one of the sides. The point where the surface changes from concave to convex is the bifurcation point, where the ball can switch from one state to another with a small push.

A bifurcation can also occur in more complex systems, such as dynamical systems that evolve over time. For example, consider a pendulum that is driven by an external force. Depending on the frequency and amplitude of the force, the pendulum can have different patterns of motion: either swinging back and forth or rotating around. The point where the motion changes from periodic to chaotic is another example of a bifurcation point.

Bifurcations are ubiquitous in nature and science, and they can be classified into different types depending on how the system changes near the bifurcation point. One common type is called a cusp bifurcation, which occurs when a system can have either one or three stable states depending on two parameters.

For example, consider a spring that is attached to a magnet and placed near another magnet. Depending on the distance and orientation of the magnets, the spring can have one equilibrium length or two possible lengths (one longer and one shorter). The region where the system has three stable states is called the cusp region, and it has a characteristic shape like a mountain peak.

How Do Proteins and Hummingbird Beaks Use Bifurcations?

Proteins are biological molecules that perform various functions in living cells by changing their shapes in response to different signals. For example, some proteins act as enzymes that catalyze chemical reactions, while others act as receptors that bind to specific molecules. Proteins are made of long chains of amino acids that fold into complex three-dimensional structures. The shape and function of a protein depend on its interactions with other molecules and its environment.

Proteins can be thought of as machines that hop between different states by changing their shapes slightly. These states correspond to different configurations of the amino acid chain that are stable or metastable (i.e., stable for a long time but not indefinitely). The transitions between these states are often triggered by small changes in parameters such as temperature, pH, or concentration of other molecules. These parameters can affect the energy landscape of the protein, which is a representation of how much energy it takes to maintain a certain shape.

The energy landscape of a protein can have multiple valleys and peaks that correspond to different states. The lowest valley is usually the most stable state (also called the native state), while higher valleys are less stable states (also called non-native states). The transitions between these states involve crossing energy barriers that separate them. The height and width of these barriers determine how easy or difficult it is for the protein to switch between states.

Some proteins use bifurcations to switch between states more efficiently. For example, some proteins have cusp bifurcations in their energy landscapes, where they can have either one or three stable states depending on two parameters. By tuning these parameters, the protein can control the height and width of the energy barriers, and thus the speed and probability of the transitions. This way, the protein can perform different functions by changing its shape in a coordinated and robust manner.

Hummingbirds are birds that can hover and fly backwards by flapping their wings at high frequencies. They also have long and slender beaks that they use to feed on nectar from flowers. Hummingbirds can open and close their beaks very quickly and precisely by using a mechanism that involves a cusp bifurcation.

The hummingbird’s beak is composed of two parts: the upper mandible and the lower mandible. The lower mandible is attached to the skull by a hinge joint, while the upper mandible is attached to the skull by a flexible membrane. The lower mandible also has two muscles that control its bending and twisting motions. By contracting and relaxing these muscles, the hummingbird can change the shape and position of its beak.

The hummingbird’s beak can have either one or two stable states depending on the forces exerted by the muscles. When the muscles are relaxed, the beak is closed and has a single stable state. When the muscles are contracted, the beak is open and has two stable states: one where the upper mandible is aligned with the lower mandible, and one where the upper mandible is bent away from the lower mandible. The point where the single stable state splits into two stable states is the cusp bifurcation point.

The advantage of operating around a cusp bifurcation is that it provides a pair of key design features:

Multistability: The system can have multiple stable states that can be accessed by small changes in parameters. This allows for more functionality and versatility in performing different tasks.
Snap-through: The system can switch between states very quickly and with minimal energy input. This allows for faster and more efficient performance and response.

The hummingbird uses these features to feed on nectar more effectively. By contracting its muscles, it can open its beak and snap it into a bent state, creating a gap between the upper and lower mandibles. This gap allows the hummingbird to insert its tongue into the flower and suck up the nectar. By relaxing its muscles, it can close its beak and snap it back into an aligned state, sealing the gap and preventing the nectar from leaking out.

How Can We Design Micro Machines Using Bifurcations?

The Cornell research team has developed a new way to design micro machines using bifurcations as a guiding principle. They call this approach bifurcation instructed design (BID). BID involves identifying bifurcations in natural or artificial systems, understanding their underlying mechanisms, and applying them to create novel micro machines that can perform complex tasks at the nanoscale.

The team has demonstrated BID by creating several examples of micro machines that operate around cusp bifurcations. These machines are made of thin sheets of magnetic materials that are patterned with cuts and folds. By applying magnetic fields, they can change their shapes and switch between different states.

One example is a micro robot that can morph into different shapes, such as a star, a cross, or a square. This robot is composed of four triangular units that are connected by hinges. Each unit has two stable states: flat or folded. By applying magnetic fields, each unit can switch between these states independently or collectively, resulting in 16 possible shapes for the robot.

Another example is a micro switch that can turn on or off an electrical circuit. This switch is composed of two beams that are connected by a hinge. Each beam has two stable states: straight or bent. By applying magnetic fields, each beam can switch between these states independently or collectively, resulting in four possible configurations for the switch.

These examples show how BID can enable the design of micro machines that have multiple functions, high performance, and low energy consumption. The team hopes that BID will inspire more innovations in microscale engineering and open new possibilities for applications in various domains.

Conclusion

Bifurcations are mathematical phenomena that occur when systems change their behavior or structure abruptly as a result of small changes in parameters. Bifurcations are widely used by natural systems, such as proteins and hummingbird beaks, to perform complex functions by switching between different states with minimal energy input.

A Cornell research team has developed a new way to design micro machines using bifurcations as a guiding principle. They call this approach bifurcation instructed design (BID). BID involves identifying bifurcations in natural or artificial systems, understanding their mechanisms, and applying them to create novel micro machines that can switch between different states with minimal energy input.

The team has demonstrated BID by creating several examples of micro machines that operate around cusp bifurcations. These machines are made of thin sheets of magnetic materials that are patterned with cuts and folds. By applying magnetic fields, they can change their shapes and switch between different states.

The team has also shown how BID can be used to create more complex micro machines that can perform logic operations, store information, and communicate with each other. These machines could have many applications in fields like biotechnology, medicine, robotics, and computing.

The team’s work is a remarkable example of how nature can inspire human innovation and how mathematics can guide engineering. By using bifurcations as a design principle, the team has opened a new frontier for microscale engineering and created a new way to explore the physics of complex systems.

We hope you enjoyed reading this article and learned something new about how hummingbird beaks inspire future micro machine design. If you want to learn more about this topic, you can check out the original paper or watch this video by the Cornell research team. Thank you for your attention and have a great day! 😊

References

Hummingbird Beak Points the Way to Future Micro Machine Design | Technology Networks
Hummingbird beak points the way to future micro machine design | Phys.org
Hummingbird beak points the way to future micro machine design | Cornell Chronicle
Hummingbird Beak Inspires Future Micro Machine Design | Mirage News
IBM Unveils World's First 2 Nanometer Chip Technology, Opening a New Frontier for Semiconductors | IBM Newsroom
Latest Advancements in Micro Nano Molding Technologies—Process ... | MDPI
Micro Technology : The Future of Electronics | Authorized Technologies

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