Understanding how the brain constructs movements remains a fundamental challenge in neuroscience. The brain may control complex movements through flexible combination of motor primitives, where each primitive is an element of computation in the sensorimotor map that transforms desired limb trajectories into motor commands. Theoretical studies have shown that a system's ability to learn action depends on the shape of its primitives. Using a time-series analysis of error patterns, here we show that humans learn the dynamics of reaching movements through a flexible combination of primitives that have gaussian-like tuning functions encoding hand velocity. The wide tuning of the inferred primitives predicts limitations on the brain's ability to represent viscous dynamics. We find close agreement between the predicted limitations and the subjects' adaptation to new force fields. The mathematical properties of the derived primitives resemble the tuning curves of Purkinje cells in the cerebellum. The activity of these cells may encode primitives that underlie the learning of dynamics.