This letter proposes a new mechanism, a four-bar linkage-based support hinge mechanism, for assisting with shoulder abduction with artificial muscle based on a shape memory alloy (SMA). An artificial muscle using the SMA coils is designed to lighten the entire system and support the wearer's movement both actively and passively. It can generate up to 273 N and 180 N with and without energy input, respectively, while weighing only 0.04 kg. Furthermore, to consider the rotation axis shifts of the arm during shoulder abduction, the trajectory of the arm along the shoulder abduction is modeled using the scapulohumeral rhythm, a combined movement of the scapula and humerus. The mechanism is designed to follow the modeled arm trajectory and achieve the required torque to perform shoulder abduction based on a four-bar linkage mechanism. It can generate up to 10.1 Nm and 6.3 Nm of torque with and without energy input, respectively. To verify the assistive effect of the proposed mechanism, electromyography is measured while performing the same exercise requiring shoulder abduction with and without the support of the mechanism. The results show that the proposed mechanism reduces not only muscle load but also fatigue while performing the shoulder abduction.