This paper presents a mathematical model that predicts both the qualitative and quantitative details of large-amplitude, voluntary movements performed by primates at intermediate speeds. The model is based on observations of muscle mechanics and behavioral organization, formulating a "virtual position" determined by muscle states. The goal is to minimize accelerative transients, which is formalized using dynamic optimization theory to determine the movement that minimizes jerk (the rate of change of acceleration). The model describes the dynamics of the movement execution and the organization of the movement separately. The criterion function, which models the goal of minimizing jerk, is derived using variational calculus. The resulting trajectory is a fifth-order polynomial in time. The model is validated through digital simulations and matches experimental data, providing insights into the planning and organization of voluntary movements. The minimum-jerk criterion function is shown to be a powerful organizing principle for a wide range of movements, from saccadic eye movements to complex arm trajectories.This paper presents a mathematical model that predicts both the qualitative and quantitative details of large-amplitude, voluntary movements performed by primates at intermediate speeds. The model is based on observations of muscle mechanics and behavioral organization, formulating a "virtual position" determined by muscle states. The goal is to minimize accelerative transients, which is formalized using dynamic optimization theory to determine the movement that minimizes jerk (the rate of change of acceleration). The model describes the dynamics of the movement execution and the organization of the movement separately. The criterion function, which models the goal of minimizing jerk, is derived using variational calculus. The resulting trajectory is a fifth-order polynomial in time. The model is validated through digital simulations and matches experimental data, providing insights into the planning and organization of voluntary movements. The minimum-jerk criterion function is shown to be a powerful organizing principle for a wide range of movements, from saccadic eye movements to complex arm trajectories.