This paper proposes a novel reconfigurable exoskeleton for ankle rehabilitation, which is capable of realizing both static and dynamic rehabilitation exercises. The conceptual design is based on a reduced representation that regards the ankle–foot complex as a movable spherical joint, so as to better replicate the physical scenario. The screw theory-based analysis results indicate that in both rehabilitation modes, the proposed exoskeleton is capable of auto-matching its rotation center with that of the ankle complex no matter how the latter moves, once it is worn by the patients. In the 2-degrees-of-freedom (DOF) rehabilitation configuration, an analysis based on a 15-point reduced model provides the basis for assessing the kinematics performance in a case where the motion of complex's center is considered. Also, the results verify that the achieved workspace can always cover the prescribed rotation range without generating singularities, as long as the center moves within the defined cylindrical area. The demonstrated 3-DOF rehabilitation configuration possesses a partially decoupled-control capability. The singularity surface can be effectively expelled from the prescribed workspace by rotating the brace. Besides, the exoskeleton's dexterity varies smoothly in the whole workspace, and its performance can be further improved by evenly distributing the drive links.