Analysis of an Actuated Two Segment Leg Model of Locomotion

Research studies on dynamic models of legged locomotion have generally focused on telescoping-type leg models. Such telescoping spring loaded inverted pendulum (SLIP) models have been able to accurately predict observed center of mass (CoM) trajectories. There have been comparatively fewer studies on dynamics of locomotion with segmented legs. Some earlier studies on the dynamics due to leg segmentation appear straightforward. For example, a simple model with the only joint moment being due to a passive springy knee has been shown to behave similarly to a telescoping spring-mass model. However, in real-life animal locomotion, there are multiple joint-moments acting at the hip, knee and the ankle joints. The joint-moments could act together to cause the whole body dynamics to diverge from those of the canonical telescoping spring mass model. The focus of this thesis is to understand the combined effect when hip and knee moments act together. In particular, this work will analyze a lumped mass two segment leg model with a hip-torque actuation and a passive sprung knee. Such mechanisms also represent real life scenarios such as motions of above knee amputees with a passive knee prosthetic. A key finding is that the governing equations for the two-segment (knee) version have a distinct structure when compared to the telescoping version of SLIP. The two segment model with a knee spring influences forces acting on the mass center in a more complex way and, unlike the telescoping leg, leads to an active force along the leg. The effect of this active force on the whole body dynamics can have an overall similar outcome to that of a spring component acting along the leg, and so is capable of replacing the spring at the knee. This result also implies that when hip moment and knee moment act together a lower knee moment or effective knee stiffness may be required compared to what studies containing only knee moments predict. This has potential application in predicting human knee and hip moment function, as well as in the design of human joint orthotics and the joints of prosthetic leg devices, as well as segmented robot legs. The actuated two segment model is capable of wide variations in behavior depending on the knee spring resting position (knee position for undeformed leg). For lower knee resting angles, it exhibits stability characteristics very similar to the telescoping SLIP, however the system stability gradually reduces as the knee resting angle is increased. Simulating the dynamics of locomotion when the knee resting angle is greater than 130introduces new complications such as singularities associated with complete leg extension, and such behaviors are categorized and defined. Overall, the model behavior with small knee angles oers one explanation for how animals with multi-segmented legs could generate whole-body locomotion dynamics similar to those predicted by telescoping hip-actuated SLIP models. However, the effect of increasing knee angles also suggests that the larger knee angles of humans may result in reduced inherent stability of locomotion, in addition to additional complicating factors due to the kinematics of full leg extension and over-extension