Whilst there are certainly features that the weapon in the sketch has in common with modern artillery, it may be stretching things a little too far to call the gun shown the forerunner of the modern day machine gun.
There is a certain modern keenness to attribute almost every modern invention to one of Da Vinci's sketches, some critics have also tried to do this with the helicopter and other modern aircraft.
Nevertheless, the sketch is another example of just how wide Da Vinci's mind ranged during his lifetime and his aptitude for technical drawings as well as the paintings for which he is best known.
Da Vinci believed that the main problem with the cannons of his time was how long it took to load and fire them. Modern machine guns and larger artillery weapons get around this issue by firing multiple bullets or shells one after the other at high speed. Da Vinci solved the problem by placing 33 small calibre guns in a row, one beside the other in three vertically stacked rows of 11.
His theory was that prior to battle all 33 weapons could be loaded. Once the first 11 guns at the top of the weapon had been fired, the guns would then be rotated, which would allow the first set to be quickly reloaded whilst the second and then third set took over firing duties.
This way, the weapon could be constantly in use, despite the relatively long loading times which were associated with weapons of the time period.
Da Vinci's approach of using more of existing weaponry, rather than fixing the fundamental issue which gave rise to the problem would be adopted by the manufacturers of early machine guns. It was only in the late 19th and particularly the early 20th Century, with the invention of modern firing mechanisms, when the problem of slow loading mechanism would be properly addressed.
The sketch is relatively devoid of notes. In some of Da Vinci's other works, his notes and other scribblings give us insight into his life and his thoughts on how his drawing would be interpreted by others. This relative lack of notes may have actually increased the popularity and notoriety of this particular drawing as it has allowed modern interpreters to see exactly what they want. The lack of detail makes it easier to compare the weapon shown to its modern day counterparts than it might otherwise have been.
Whilst it's possible to overstate the amount of foresight shown in Da Vinci's 33 barrelled organ or machine gun drawing, it remains an example of Da Vinci's ability to solve some of the biggest and most fundamental problems of his age.