Fatma Zeynep Temel

Characterization and Modeling of Biomimetic Untethered Robots Swimming in Viscous Fluids Inside Circular Channels

Miniaturized robots with bioinspired propulsion mechanisms, such as rotating helical flagella, are promising tools for minimally invasive surgery, diagnosis, targeted therapy, drug delivery, and removing material from the human body. Understanding the locomotion of swimmers inside fluid-filled channels is essential for the design and control of miniaturized robots inside arteries and conduits of living organisms. In this paper, we describe scaled-up experiments and modeling of untethered robots with a rotating helical tail and swimming inside a tube filled with a viscous fluid. Experiments mimic low Reynolds number swimming of miniaturized robots inside conduits filled with aqueous solutions. A capsule that contains the battery and a small dc motor is used for the body of the robots. Helical tails with different geometric parameters are manufactured and used to obtain swimming speeds and body rotation rates of robots inside the cylindrical channel. Three-dimensional incompressible flow around the robot inside the channel is governed by Stokes equations, which are solved numerically with a computational fluid dynamics (CFD) model. Predicted velocities of robots are compared with the experimental results for the validation of the CFD model, which is used to analyze effects of the helical radius, pitch, and the radial position of the robot on the swimming speed, forces acting on the robot, and efficiency.

Comparison on experimental and numerical results for helical swimmers inside channels

Swimming micro robots are becoming feasible in biomedical applications such as targeted drug delivery, opening clogged arteries and diagnosis owing to recent developments in micro and nano manufacturing technologies. It has been demonstrated at various scales that micro helices with magnetic coating or attached to a magnet can move in fluids with the application of external rotating magnetic fields. The motion of micro swimmers interacting with flow inside channels needs to be well understood especially for medical applications where the motion of micro robots inside arteries and conduits in the body become pertinent. In this work, swimming of helical micro robots with magnetic heads inside tubes is modeled with the resistive force theory (RFT) and validated with experiments conducted in glycerin filled mini glass channels placed in rotational magnetic fields. The time-averaged forward velocities of magnetically driven micro swimmers that are calculated by the RFT model agree very well with experimental results.

The milliDelta: A high-bandwidth, high-precision, millimeter-scale Delta robot

A high-bandwidth, millimeter-scale Delta robot offers precise control for microscale applications. Delta robots have been widely used in industrial contexts for pick-and-place applications because of their high precision and speed. These qualities are also desirable at the millimeter scale for applications such as vibration cancellation in microsurgery and microassembly or micromanipulation. Developing a millimeter-scale Delta robot that maintains the characteristic input-output behavior and operates with high speed and precision requires overcoming manufacturing and actuation challenges. We present the design, fabrication, and characterization of an adapted Delta robot at the millimeter scale (the “milliDelta”) that leverages printed circuit microelectromechanical system manufacturing techniques and is driven by three independently controlled piezoelectric bending actuators. We validated the design of the milliDelta, where two nonintersecting perpendicular revolute joints were used to replace an ideal universal joint. In addition, a transmission linkage system for actuation was introduced to the laminate structure of the milliDelta. This 15 millimeter–by–15 millimeter–by–20 millimeter robot has a total mass of 430 milligrams and a payload capacity of 1.31 grams and operates with precision down to ~5 micrometers in a 7.01-cubic-millimeter workspace. In addition, the milliDelta can follow periodic trajectories at frequencies up to 75 hertz, experiencing velocities of ~0.45 meters per second and accelerations of ~215 meters per squared second. We demonstrate its potential utility for high-bandwidth, high-precision applications that require a compact design.

Navigation of mini swimmers in channel networks with magnetic fields

Controlled navigation of swimming micro robots inside fluid filled channels is necessary for applications in living tissues and vessels. Hydrodynamic behavior inside channels and interaction with channel walls need to be understood well for successful design and control of these surgical-tools-to-be. In this study, two different mechanisms are used for forward and lateral motion: rotation of helices in the direction of the helical axis leads to forward motion in the viscous fluid, and rolling due to wall traction results with the lateral motion near the wall. Experiments are conducted using a magnetic helical swimmer having 1.5 mm in length and 0.5 mm in diameter placed inside two different glycerol-filled channels with rectangular cross sections. The strength, direction and rotational frequency of the externally applied rotating magnetic field are used as inputs to control the position and direction of the micro swimmer in Y- and T-shaped channels.

The principles of cascading power limits in small, fast biological and engineered systems

Hop, skip, jump, or massive leap In biological and engineered systems, an inherent trade-off exists between the force and velocity that can be delivered by a muscle, spring, or combination of the two. However, one can amplify the maximum throwing power of an arm by storing the energy in a bow or sling shot with a latch mechanism for sudden release. Ilton et al. used modeling to explore the performance of motor-driven versus spring-latch systems in engineering and biology across size scales. They found a range of general principles that are common to animals, plants, fungi, and machines that use elastic structures to maximize kinetic energy. Science, this issue p. eaao1082 Combining motors, springs, and latches offers many routes to optimization of mechanical power in biological and engineered systems. INTRODUCTION Mechanical power, whether for launched missiles or running humans, is limited by the universal, physical trade-off between force and velocity. However, many biological systems use power-amplifying mechanisms that enable unmatched accelerations in challenging environments and across a wide range of size scales. How these mechanisms actually enhance power output remains unclear. Power-amplified biological systems are of particular interest because they achieve a trio of combined capabilities that exceed current engineering performance: (i) high accelerations that (ii) can be continuously fueled through metabolic processes and (iii) are used repeatedly with minimal performance degradation throughout the life of the organism. Although engineers have struggled to design lightweight and long-lasting devices that can deliver high power output, biological systems have been performing such feats for millions of years and using these systems for a myriad of functions. RATIONALE Through a mathematical analysis that is equally applicable to biological and synthetic systems, we investigate how power enhancement emerges through the dynamic coupling of motors, springs, latches, and projectiles and relate the findings to data on existing biological and engineered systems. The model incorporates nonideal behavior of spring and latch systems in a scalable framework using both dimensional and dimensionless approaches. RESULTS Motors, springs, and latches all experience force-velocity trade-offs, and their integration exemplifies the cascading effects of power limits. Springs circumvent motor power limits when projectile mass is small and the motor’s force-velocity dynamics limit performance. However, springs also exhibit force-velocity trade-offs when their mass, mechanical properties, and time dependence are incorporated. Latches dynamically modulate spring power through variation in latch shape and velocity. Motor-driven and spring-driven movements are distinct in their transitions across performance (power, maximum velocity, and duration), which are largely dictated by projectile mass. When analyzed as a single, integrated system, the necessity for tuning and inherent tunability are evident. Simply increasing the force output of a motor does not enhance performance; the spring and latch capacities must also shift. Simply decreasing the size of the system also does not enhance performance; spring energy storage falls off at smaller scales due to the effects of materials, stiffness, and geometry. With this mathematical foundation of scaling and integration, we apply a new lens to patterns of biological scaling limits and propose new design principles for integrated and tuned systems. CONCLUSION Our model reveals a foundational framework for the scaling, synthetic design, and evolutionary diversification of power-amplified systems. The model enables a straightforward approach to analyzing biological systems, encourages a rich design space and functionality for synthetic systems, and highlights a compelling need for the integrative analysis of spring and latch dynamics in both synthetic and biological systems. Power-amplified biological and synthetic systems use spring elements to drive motion over a range of size scales. Mathematical modeling reveals a cascade of power limits and mass-dependent transitions in power delivery that arise from the integration of motors, springs, and latches to actuate movement. Variation of these components creates synergistic effects relevant to the analysis and synthesis of diverse power-amplified systems. Mechanical power limitations emerge from the physical trade-off between force and velocity. Many biological systems incorporate power-enhancing mechanisms enabling extraordinary accelerations at small sizes. We establish how power enhancement emerges through the dynamic coupling of motors, springs, and latches and reveal how each displays its own force-velocity behavior. We mathematically demonstrate a tunable performance space for spring-actuated movement that is applicable to biological and synthetic systems. Incorporating nonideal spring behavior and parameterizing latch dynamics allows the identification of critical transitions in mass and trade-offs in spring scaling, both of which offer explanations for long-observed scaling patterns in biological systems. This analysis defines the cascading challenges of power enhancement, explores their emergent effects in biological and engineered systems, and charts a pathway for higher-level analysis and synthesis of power-amplified systems.

Changes in the flagellar bundling time account for variations in swimming behavior of flagellated bacteria in viscous media

Significance Changes in the swimming speed and behavior of wild-type Escherichia coli in Newtonian fluids of varying viscosity are described. Individual cells exhibit both “run-and-tumble” and “slow random-walk” modes of motility. As the solution viscosity rises, variations in the flagellar bundling time account for changes in the swimming behavior of the cells. A unique contribution is the identification of the skewness of the speed distribution as a key parameter for characterizing different swimming behaviors. The skewness is shown to be solely a function of viscosity and independent of the cell’s metabolic activity. Using both numerical simulation and resistive force theory, we compute the flagellar bundling time as a function of viscosity and achieve good agreement with direct observations. Although the motility of the flagellated bacteria, Escherichia coli, has been widely studied, the effect of viscosity on swimming speed remains controversial. The swimming mode of wild-type E. coli is often idealized as a run-and-tumble sequence in which periods of swimming at a constant speed are randomly interrupted by a sudden change of direction at a very low speed. Using a tracking microscope, we follow cells for extended periods of time in Newtonian liquids of varying viscosity and find that the swimming behavior of a single cell can exhibit a variety of behaviors, including run and tumble and “slow random walk” in which the cells move at a relatively low speed. Although the characteristic swimming speed varies between individuals and in different polymer solutions, we find that the skewness of the speed distribution is solely a function of viscosity and can be used, in concert with the measured average swimming speed, to determine the effective running speed of each cell. We hypothesize that differences in the swimming behavior observed in solutions of different viscosity are due to changes in the flagellar bundling time, which increases as the viscosity rises, due to the lower rotation rate of the flagellar motor. A numerical simulation and the use of resistive force theory provide support for this hypothesis.