Currently there are nearly 2 million people living with limb loss in the United States [1]. Many of these individuals are either transtibial (below knee) or transfemoral (above knee) amputees and require an ankle-foot prosthesis for basic mobility. While there are an abundance of options available for individuals who require an ankle-foot prosthesis, these options fail to mimic an intact ankle when it comes to key evaluation criteria such as range of motion, push-off force, and roll over shape. The roll over shape is created by plotting the center of pressure during a step in a shank-based coordinate system. To address the need for a prosthesis that effectively replaces the ankle's contribution to an able-bodied gait, a biomimetic approach is taken in the design the Compliant & Articulating Prosthetic Ankle (CAPA) foot. The passive CAPA foot consists of four components connected by torsion springs representing the Phalanges, Metatarsal bones, Talus, and Calcaneus. Biomimetic functionality is exhibited by CAPA foot with regards to the roll over shape and a linear relationship between moment exerted and ankle angle, distinguishing the CAPA foot from other ankle-foot prostheses. A mathematical model of the CAPA foot is created to determine the roll over shape a specific CAPA foot geometry would produce and support eventual customization of the 3D printed components. The mathematical model is used to optimize the design to two distinctly different roll over shapes, one with a rocker radius closer to that of the Talus bone and the other closer to the energetically advantageous value of 0.3 times leg length [2, 3]. Compliant and stiff versions of the two CAPA feet were compared to a conventional Solid Articulating Cushioned Heel (SACH) foot and a passive dynamic response foot (Renegade® AT produced by Freedom Innovations). Ten able bodied subjects walked on the Computer Assisted Rehabilitation Environment normally, and then with a transfemoral prosthetic simulator. The study was separated into two experiments. For the second experiment (subjects 6-10), the versions of the CAPA foot had pretension in the dorsiflexion springs. Overall the ankle angles and sagittal plane ground reaction forces of the CAPA foot better mimicked an intact ankle-foot than the existing passive ankle-foot prostheses. Added pretension increased the sagittal plane ground reaction forces and roll over shape radius of curvature and arc length. Nine out of ten participants preferred the CAPA foot and there was a statistical significant difference (F=14.2, p<0.01) between the difficulty level rating given for trials with the CAPA foot versus the existing ankle-foot prostheses. The mathematical model is found to be capable of accurately predicting experimental roll over shape trends and the concept of roll over shape based design is demonstrated. Successful aspects of the CAPA foot can be applied to other ankle-foot prosthesis. The CAPA foot could provide a passive, cheap, and personalizable ankle-foot prosthesis that improves mobility the quality of life for individual’s lacking an intact ankle.

Human gait is elegant and efficient in propelling the body forward. While a healthy human gait is symmetric, any deviation from symmetry can cause inefficiencies to the entire body. Such asymmetries may present themselves in hemiplegic patients, prosthetic users, lower limb injuries, limb height and weight discrepancies, or abnormal overground foot rolling. In this dissertation, practical passive methods to alleviate such asymmetric walking dynamics are presented. The novel concepts presented in this manuscript can all be related and applied to passive gait rehabilitation, that is, the rehabilitation of a person's gait through methods that do not require external power. One of the passive rehabilitation solutions for asymmetric gait is the the Gait Enhancing Mobile Shoe (GEMS). The GEMS is designed to mimic the motions of a split-belt treadmill, which is commonly used for asymmetric gait rehabilitation. Two iterations of the GEMS prototype are presented. While the first development design of the GEMS was too bulky, it showed controlled and constant backward motion. The second fully mechanical design was tested on healthy participants and was successful in producing spatial and temporal aftereffects similar to those seen in split-belt treadmill gait studies. In order to more accurately define the dynamics of the GEMS wheel as an individual steps on the shoe, mathematical models that predict the static and dynamic behavior of irregularly shaped curves on a flat plane as a weight is applied are derived and verified. While this kinetic shape concept can be applied to rolling irregularly shaped wheels, it can also be utilized to predict and manipulate roll-over motions of human feet, prosthetic feet, or even robotic biped feet. This kinetic shape concept was applied to develop a force dependent musical string instrument, transportation device, a more efficient walking crutch for controlled crutch walking, and a unique form of force mathematics. The asymmetric kinematics of dissimilar human limbs can be synchronized for symmetry with a generalized passive kinematic synchronization technique that can match the motion of two or more dissimilar and uncoupled rotating systems. This kinematic synchronization technique introduced in this dissertation can be applied to duplicate the motion of swinging human limbs with dissimilar masses and mass distributions, which allows for the passive synchronization and rehabilitation of human limbs such as swinging arms and legs during walking. This technique also allows for the synchronization of mechanical systems such as pendulums, propellers, or rotating cams. Finally, a detailed derivation of a two and three link passive dynamic walker (PDW) model with and without variable radius feet is presented. While PDW models have been studied and derived for decades, this dissertation offers a clear and complete guide on how to derive the kinematics and kinetics of the simplest compass gait, three-link point-foot, and for the first time, a variable radius foot PDW model, where the roll-over foot shape of the PDW can be dependent on its position or other kinematic variables. This advancement in the PDW model allows for the systematic evaluation of the change of various gait parameters such as foot roll-over shape or robotic foot dynamics. This numerical biped model was compared to human gait parameters. This comparison included normal walking, tied- and split-belt treadmill walking, and GEMS walking. This model was also used to analyze the dynamic effects of changing the foot roll-over parameters such as foot roll radius and foot shape curvature. In addition, the PDW model was employed to investigate the perception of normal and pathological gait. The PDW model was systematically manipulated to produce walking patterns that showed a degree of abnormality in spatial and temporal gait parameters. This analysis showed that certain gait parameters may be asymmetrically changed to some extent without causing an abnormal perception.