How dynamic interactions between nervous system regions in mammals performs online motor control remains an unsolved problem. Here we present a new approach using a minimal model comprising spinal cord, sensory and motor cortex, coupled by long connections that are plastic. It succeeds in learning how to perform reaching movements of a planar arm with 6 muscles in several directions from scratch. The model satisfies biological plausibility constraints, like neural implementation, transmission delays, local synaptic learning and continuous online learning. The model can go from motor babbling to reaching arbitrary targets in less than 10 minutes. However, because there is no cerebellum the movements are ataxic. As emergent properties, neural populations in motor cortex show directional tuning and oscillatory dynamics, and the spinal cord creates convergent force fields that add linearly. The model is extensible and may eventually lead to complete motor control simulation.