Exoskeletons show great promise in aiding people in a wide range of applications. One such application is medical rehabilitation and assistance of those with spinal cord injuries. Exoskeletons have the potential to offer several benefits over wheelchairs, including a reduction in the risk of upper-body injuries associated with extended wheelchair use. To fully mitigate this risk of injury, exoskeletons will need to be fully self-balancing, able to move and stand without crutches or other walking aid. To accomplish this, the Orthotic Lower-body Locomotion Exoskeleton (OLL-E) will actuate 12 Degrees of Freedom, six in each leg, using custom design linear series elastic actuators. The placement of these actuators relative to each joint axis, and the geometry of the linkage connecting them, were critical to ensuring each joint was capable of producing the required outputs for self-balancing locomotion. In pursuit of this goal, a general model was developed, relating the actuator's position and linkage geometry to the actual joint output over its range of motion. This model was then adapted for each joint in the legs and compared against the required outputs for humans and robots moving through a variety of gaits. This process allowed for the best placement of the actuator and linkages within the design constraints of the exoskeleton. The structure of the exoskeleton was then designed to maintain the desired geometry while meeting several other design requirements such as weight, adjustability, and range of motion. Adjustability was a key factor for ensuring the comfortable use of the exoskeleton and to minimize risk of injury by aligning the exoskeleton joint axes as close as possible to the wearer's joints. The legs of OLL-E can accommodate users between 1.60 m and 2.03 m in height while locating the exoskeleton joint axes within 2 mm of the user's joints. After detailed design was completed, analysis showed that the legs met all long-term goals of the exoskeleton project.