This article presents the design of a rehabilitation exoskeleton, which, based on a single actuator and a bar mechanism, emulates human gait for subjects between 40 and 50 years old. For the design, simulation tools as Linkage were used to establish the initial configuration of the mechanism (similar to human biomechanics) and verify that the behavior of the final link was in accordance with the movement of human gait. Then, using Matlab and Newton Raphson, the system of equations that describes the mechanism kinematics was solved to obtain X and Y coordinates of the joints that describe the position of the hip and knee at different periods of time, and these were compared with studies reported in the literature. Finally, a CAD model was designed and imported into Matlab with the Simscape Multibody tool in order to evaluate if the behavior of the designed prototype agrees with the pre-established mathematical calculations. Furthermore, a PID controller is designed to obtain the desired behaviors in the input link, considering that, in order to take a single step, it must start and end with a speed equal to zero degrees/second, and have covered the 360 degrees required to execute the complete gait of a single foot, considering the average cadence of human walking. As a results, the mathematical model, simulation and control of a bar mechanism that emulates human gait pattern for people with leg length from 90 cm to 100 cm is presented.