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Forward dynamic simulation is used to examine the causal relationships between muscle excitation patterns and human movement. The computed muscle control (CMC) algorithm computes a set of muscle excitations for a movement using proportional-derivative control. However, errors between experimental and simulated kinematics may cause rapid movements. Herein, we propose a novel algorithm, i.e., hybrid computed muscle control (HCMC), which uses a hybrid of numerical integration and optimization to compute muscle excitation patterns that accurately track kinematics, even for rapid movements. We compared the muscle excitation patterns and accuracies of the kinematics simulated by HCMC and CMC using synthetic and experimental data. Two simple musculoskeletal models were used. The synthetic data were generated for three repetitive movements from the rest position to the flexed position (the hip, knee, and ankle underwent 10°, 20°, and 10° plantar flexion, respectively) and back to the rest position for various times. Experimental data were obtained for a subject running at 220 steps/min. The maximum errors in all kinematics calculated using the HCMC algorithm were extremely lower than those calculated using CMC algorithm (HCMC: 0.04–0.07° [synthetic data] and 0.00–0.03° [experimental data]; CMC: 1.04–2.41° [synthetic data] and 0.48–2.50 [experimental data]). For rapid movements, muscle excitations estimated using HCMC occurred early and without delay than those estimated using CMC. The HCMC algorithm can provide muscle excitation patterns that accurately track kinematics and may be useful for perturbation studies using forward dynamic simulation of joints characterized by a low range of motion during rapid movements. [ABSTRACT FROM AUTHOR]