Date of Award

Fall 2014

Degree Type


Degree Name

Master of Science (MS)


Mechanical Engineering

First Advisor

Justin E. Seipel

Committee Member 1

Raymond J. Cipra

Committee Member 2

Xinyan Deng


In human running, the ankle, knee, and hip moments are known to play different roles to influence the dynamics of locomotion. A recent study of hip moments and several hip-based legged robots have revealed that hip actuation can significantly improve the stability of locomotion, whether controlled or uncontrolled. Ankle moments are expected to also significantly affect running stability, but in a different way than hip moments. Here we seek to advance the current theory of dynamic running and associated legged robots by determining how simple open-loop ankle moments could affect running stability. We simulate a dynamical model, and compare it with a previous study on the role of hip moments. The model is relatively simple with a rigid trunk and a springy leg to represent the effective stiffness of the knee. At the hip we use a previously established proportional and derivative controlled moment with pitching angle as feedback. At the ankle we use the simplest ankle actuation, a constant ankle torque as a rough approximation of the net positive work done by the ankle moment during human locomotion. Even in this simplified model, we find that ankle and hip moments can affect the center of mass (COM) and pitching dynamics in distinct ways. Analysis of the governing equations shows that hip moments can directly influence the upper body balance, as well as indirectly influence the center of mass translation dynamics. However, ankle moments can only indirectly influence both. Simulation of the governing equations shows that the addition of ankle moment has significant benefits to the quality of locomotion stability, such as a larger basin of attraction. We also find that adding the ankle moments generally expands the range of parameters and velocities for which the model displays stable solutions. Overall, these findings suggest that ankle moments would play a significant role in improving the quality and range of running stability in a system with a rigid trunk and a telescoping leg, which would be a natural extension of current springy leg robots. Further, these results provide insights into the role that ankle moments might play in human locomotion.