The typical function of the cerebellum is to help provide rapid turn-on signals for the agonist muscles and simultaneous reciprocal turnoff signals for the antagonist muscles at the onset of a movement. Then, upon approaching termination of the movement, the cerebellum is mainly responsible for timing and executing the turnoff signals to the agonists and the turn-on signals to the antagonists. Although the exact details are not fully known, one can speculate from the basic cerebellar circuit of Figure 1 how this process might work, as follows.

Fig1. Deep nuclear cells receive excitatory and inhibitory inputs. The left side of this figure shows the basic neuronal circuit of the cerebellum, with excitatory neurons shown in red and the Purkinje cell (an inhibitory neuron) shown in black. To the right is shown the physical relationship of the deep cerebellar nuclei to the cerebellar cortex with its three layers.
Let us suppose that the turn-on/turnoff pattern of agonist/antagonist contraction at the onset of movement begins with signals from the cerebral cortex. These signals pass through noncerebellar brain stem and cord path ways directly to the agonist muscle to begin the initial contraction.
At the same time, parallel signals are sent by way of the pontile mossy fibers into the cerebellum. One branch of each mossy fiber goes directly to deep nuclear cells in the dentate or other deep cerebellar nuclei, which instantly sends an excitatory signal back into the cerebral corticospinal motor system, either by way of return signals through the thalamus to the cerebral cortex or by way of neuronal circuitry in the brain stem, to support the muscle contraction signal that had already been begun by the cerebral cortex. As a consequence, the turn-on signal, after a few milliseconds, becomes even more powerful than it was at the start because it becomes the sum of both the cortical and the cerebellar signals. This effect is the normal effect when the cerebellum is intact, but in the absence of the cerebellum, the secondary extra supportive signal is missing. This cerebellar support makes the turn-on muscle contraction much stronger than it would be if the cerebellum did not exist.
Now, what causes the turnoff signal for the agonist muscles at the termination of the movement? Remember that all mossy fibers have a second branch that transmits signals by way of the granule cells to the cerebellar cortex and, eventually, by way of “parallel” fibers, to the Purkinje cells. The Purkinje cells in turn inhibit the deep nuclear cells. This pathway passes through some of the smallest, slowest-conducting nerve fibers in the nervous system—that is, the parallel fibers of the cerebellar cortical molecular layer, which have diameters of only a fraction of a millimeter. Also, the signals from these fibers are weak, so they require a finite period to build up enough excitation in the dendrites of the Purkinje cell to excite it. However, once the Purkinje cell is excited, it sends a strong inhibitory signal to the same deep nuclear cell that had originally turned on the movement. Therefore, this signal helps turn off the movement after a short time.
Thus, one can see how the complete cerebellar circuit could cause a rapid turn-on agonist muscle contraction at the beginning of a movement and yet cause also a precisely timed turnoff of the same agonist contraction after a given period.
Now let us speculate on the circuit for the antagonist muscles. Most important, remember that there are reciprocal agonist/antagonist circuits throughout the spinal cord for virtually every movement that the cord can initiate. Therefore, these circuits are part of the basis for antagonist turnoff at the onset of movement and then turn-on at termination of movement, mirroring whatever occurs in the agonist muscles. But also remember that the cerebellum contains several other types of inhibitory cells besides Purkinje cells. The functions of some of these cells are still to be determined; they, too, could play roles in the initial inhibition of the antagonist muscles at onset of a movement and subsequent excitation at the end of a movement.
These mechanisms are still partly speculation. They are presented here to illustrate ways by which the cerebellum could cause exaggerated turn-on and turnoff signals, thus controlling the agonist and antagonist muscles, as well as the timing.