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.

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.

Although the motility of the flagellated bacteria, , has been widely studied, the effect of viscosity on swimming speed remains controversial. The swimming mode of wild-type 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.