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In golf swing analysis, high-speed cameras and Trackman devices are traditionally used to collect data about the club, ball, and putt. However, these tools are costly and often inaccessible to golfers. This research proposes an alternative solution, employing an affordable inertial motion capture system to record golf swing movements accurately. The focus is discerning the differences between motions producing straight and slice trajectories. Commonly, the opening motion of the body’s left half and the head-up motion are associated with a slice trajectory. We employ the Hilbert–Huang transform (HHT) to examine these motions in detail to conduct a biomechanical analysis. The gathered data are then processed through HHT, calculating their instantaneous frequency and amplitude. The research found discernible differences between straight and slice trajectories in the golf swing’s moment of impact within the instantaneous frequency domain. An average golfer, a single handicapper, and three beginner golfers were selected as the subjects in this study and analyzed using the proposed method, respectively. For the average golfer, the head and the left leg amplitudes of the swing motions increase at the moment of impact of the swings, resulting in the slice trajectory. These results indicate that an opening of the legs and head-up movements have been detected and extracted as non-linear frequency components, reviewing the biomechanical meaning in slice trajectory motion. For the single handicapper, the hip and left arm joints could be the target joints to detect the biomechanical motion that triggered the slice trajectory. For the beginners, since their golf swing forms were not finalized, the biomechanical motions regarding slice trajectory were different from each swing, indicating that beginner golfers need more practice to fix their golf swing form first. These results revealed that our proposed framework applied to different golf levels and could help golfers to improve their golf swing skills to achieve straight trajectories.