Home exercise and self-served gyms allow a larger population to exercise regularly without the cost of hiring private coaches. In absence of professional guidance, however, exercisers can suffer from injuries to muscles and joints. High-precision, affordable arm tracking with commercial, off-the-shelf (COTS) wearable devices has become an urgent need to prevent workout injuries and improve exercise performance. Recent studies with inertial measurement units (IMUs) or audio signals are neither computationally feasible for real-time motion tracking with satisfactory accuracy using COTS devices nor practically usable due to the interference with noisy ambient environments. In this paper, we propose UltraMotion, a real-time, high-precision ultrasonic arm motion tracking system designed for practical use. UltraMotion performs point cloud queries based on hidden Markov models (HMMs), a novel ultrasonic acoustic ranging method, and an extended Kalman filter (EKF) to predict the locations of all three arm joints, making it the first system offering shoulder locations. Experimental results with only a smartphone and a smartwatch demonstrate the effectiveness of UltraMotion in tracking shoulder, elbow, and wrist locations with impressively small median errors of 6.4 cm, 7.1 cm, and 8.5 cm in real-world environments, outperforming all previous systems, making UltraMotion an ideal choice for daily exercise.