Most individuals who experience a stroke exhibit several sensorimotor impairments that limit their independence in everyday activities. Hemiparetic gait is frequently characterized by reduced knee flexion in swing due to knee stiffness or muscle weakness and knee hyperextension or knee buckling in the stance phase. Recently, unilateral-powered orthoses have been designed to overcome the limitations of the passive knee-ankle-foot orthoses. This study presents a unilateral Active Knee Orthosis Exoskeleton, AKO-$\beta$, endowed with a series elastic actuator and designed to assist the knee in flexion and extension movements. The paper describes the system mechatronic design and its characterization on the bench, the control system, and pilot experiments with three post-stroke participants. The device has a weight of 1.78 kg on the user's leg, with a lateral encumbrance of 76 mm. The pilot experiments aimed to verify the effects of the exoskeleton assistance in hemiparetic gait patterns. When walking with the device, participants on average increased the knee flexion on the paretic side by 18.70 deg (+44.9%) during swing and decreased knee hyperextension in stance by 4.50 deg, compared to walking without it. Overall, when walking with the exoskeleton, subjects showed improved Gait Variable Score of the paretic knee profile by 37.5% compared to walking without it. The temporal and spatial gait symmetry indexes did not show clear changes, although an improvement in symmetry was observed in two of the three participants. These preliminary results suggest the potential benefits of the unilateral Active Knee Orthosis exoskeleton to enhance and restore mobility in individuals with hemiparetic gait.