The self-aligning capability of an exoskeleton is important to ensure wearing comfort, and the delicate motion ability of the exoskeleton is essential for motion assistance. Designing a self-aligning exoskeleton that offers improved wearing comfort and enhanced motion-assistance functions remains a challenge. This paper proposes a novel spatial self-aligning mechanism for a knee exoskeleton to enable simultaneous assistance in the flexion and extension (FE) of the knee joint and the internal and external rotation (IER) of the hip joint. Additionally, considering the misalignment of the human-robot joint axes, a kinematic model of the knee exoskeleton is established and analyzed to demonstrate the kinematic compatibility of the exoskeleton. Furthermore, a global torque manipulability (GTM) index is proposed to evaluate the effects of dimensional parameters on the exoskeleton's performance, and then the knee exoskeleton is optimized according to the GTM index. Finally, experiments are conducted to validate the performance of the proposed exoskeleton. The experimental results show that during knee FE and hip IER, the proposed exoskeleton exhibits lower interaction forces and torques than existing exoskeletons.