The design of an innovative spherical mechanism with three degrees of freedom for a shoulder joint exoskeleton is presented in this paper. The spherical mechanism is designed with a double parallelogram linkage, which connects two revolute joints to implement the motion as a spherical joint, while maintaining the remote center of rotation. The design has several new features compared to the current state-of-the-art: (1) a relative large range of motion free of singularity, (2) high overall stiffness, (3) lightweight and (4) compact, which make it suitable for assistive exoskeletons.