Power Limits of Repeatable Movement in Small, Fast Organisms: Guiding Principles for Engineering Design*

Many biological systems incorporate spring and latch elements to enhance power output. These power-amplified biological systems can exceed current engineering performance: they produce high accelerations that can be continuously fueled through metabolic processes, and are used repeatedly with minimal performance degradation. In this work, we establish a framework for analyzing power amplified systems. We model how power enhancement emerges through the dynamic coupling of motors, springs, and latches, each of which displays its own force-velocity behavior. This approach reveals a rich and tunable performance landscape for spring-actuated movement that is applies to biological and synthetic systems. By including non-ideal springs and latches, we identify critical transitions in mass that depend on the materials properties and geometry of the spring and latch components. Analyzing the components as a single, integrated system, reveals the necessity for tuning and inherent tunability of the system. The integration of mathematical, physical, engineering, and biological approaches illuminates the interdependence of power enhancing components and their effects in biological and engineered systems.