Bipedal robotic locomotion based on passive dynamics is a field that has been extensively researched. By exploiting the natural dynamics of the system, these bipedal robots consume less energy and require minimal control to take a step. Yet the design of most of these bipedal machines is inherently unstable and difficult to control since there is a tendency for the machine to fall once it stops walking. This thesis presents the design and analysis of a novel three-legged walking robot for a single step. The STriDER (Self-excited Tripedal Dynamic Experimental Robot) incorporates aspects of passive dynamic walking into a stable tripedal platform. During a step, two legs act as stance legs while the other acts as a swing leg. A stance plane, formed by the hip and two ground contact points of the stance legs, acts as a single effective stance leg. When viewed in the sagittal plane, the machine can be modeled as a planar four link pendulum. To initiate a step, the legs are oriented to push the center of gravity outside of the stance legs. As the body of the robot falls forward, the swing leg naturally swings in between the two stance legs and catches the STriDER. Once all three legs are in contact with the ground, the robot regains its stability and the posture of the robot is then reset in preparation for the next step. To guide the design of the machine, a MATLAB simulation was written to allow for tuning of several design parameters, including the mass, mass distribution, and link lengths. Further development of the code also allowed for optimization of the design parameters to create an ideal gait for the robot. A self-excited method of actuation, which seeks to drive a stable system toward instability, was used to control the robot. This method of actuation was found to be robust across a wide range of design parameters and relatively insensitive to controller gains. / Master of Science