St. Pierre, RyanThis dissertation presents work towards understanding the role of legs in loco- motion for robots with a body mass of 1 g to 1 mg. Locomotion models such as the inverted pendulum model and the spring loaded inverted pendulum model provide insight into the design parameters and control of legged robots. However, as body mass scales down, below 1 g, the inertial forces required in these models to either propel the next steps or compress a spring begin to vanish, requiring an understand- ing of how legged locomotion differs between scales. To this end, an experimental methodology is presented using physical models focusing solely on the mechanical aspects of locomotion at this scale to understand and develop relevant locomotion models. At the gram-scale, a new experimental methodology is developed utilizing 3D printed robots and permanent magnets for actuators. This technique enables studies on the role of gait and the viscoelastic properties of the robot’s legs. By choosing a well tuned leg, with favorable compliance and damping, and a leg-dominated gait, gram-scale legged running robots were demonstrated running at speeds up to 11.7 body lengths per second. The leg compliance and damping design space is explored in a torque-driven spring loaded inverted pendulum model to better understand the trade-offs between robot speed, stability, and efficiency. The physical platform is scalable with the availability of magnetic material and printing. In this work, robots are scaled down to 1 mg in body mass, allowing locomotion to be studied at body masses 1,000 times smaller than before. This work demonstrates a robot running at speeds up to 15 body lengths per second and further modifications demonstrated speeds over 35 body lengths per second. Using this platform, the mechanics and ground reaction forces of a milligram-scale runner were measured, showing a locomotion profile similar to a grounded torque-driven spring loaded inverted pendulum model. Using observations from the experimental work, this model was numerically simulated, giving insight into how leg compliance is used for a grounded running model. For example, the simulation shows that leg compression increases speed, but does not necessarily propel the next steps as with a traditional spring loaded inverted pendulum model. Bringing together the experimental insights with the numerical model provides a road map for exploiting passive dynamics in robots at sub-gram scales.enDissertationRoboticsMechanical engineering