During activities of daily living (ADLs), the wrist is mainly engaged in positioning and directing the hand. Researches have demonstrated that restoring wrist mobility can significantly enhance the manipulation ability, reduce body distortion caused by motion compensation, and improve the quality of life for amputees. However, most daily activities, particularly the delicate ones, place high demands on the ability of wrist to maintain a certain rotation angle, also known as non-back-drivable ability, which poses a challenge to the design of prosthetic wrists. To address this issue, various solutions have been proposed, including motor holding brakes, high reduction ratio reducers, and worm gears. However, the motor holding brake only functions after a power outage and cannot continuously prevent torque from the load end. The latter two solutions may alter the transmission ratio, resulting in reduced movement speed and transmission efficiency. Therefore, how to design a miniaturized non-back-drivable mechanism without changing the transmission ratio so that the forearm rotational freedom can be locked at any position for any duration is a problem to be solved in the research of prosthetic wrist designs. This paper presents a line-contact based non-back-drivable clutch (NBDC) that does not cause changes in the transmission ratio, ensuring the motion performance of the prosthetic limb. At the same time, it does not introduce additional friction in the forward transmission process, guaranteeing the overall efficiency. Most importantly, it only allows the torque transmitting from the motor to the load, prevents the load reversely from driving back even in a power failure condition, significantly improving the stability, safety, and comfort. Detailed kinematic and static analyses of the working process has been conducted, and transient dynamics simulation has been performed to verify its effectiveness. Through experiments, it is demonstrated that the self-locking torque of the output end could reach approximately 600 Nmm, and the unlocking torque of the input end is about 80 Nmm, which can be effectively integrated in prosthetic wrist rotation joints, contributing to the performance, safety and energy saving of prosthetic joint systems.