At least according to wikipedia, the frontal lobe houses the primary motor cortex, but in a different article about the cerebellum, it says the cerebellum controls motor function. So, do both parts control voluntary movement at once? What's the difference in the roles these two parts play in movement?
Cortex stores movement memory, basal ganglia is responsible for "chunking", or segmenting the memory, and cerebellum compares cortex memory and current movement to correct for errors and to update perception of movement. So to answer your question they all control different components/processes of learned movements at the same time and in conjunction.