Our founders weren't concerned with types of weapons. They were concerned with a centralized government having a monopoly on the use of force.
This is from an article I read recently:
A people cannot simultaneously live free and be bound to any human master or man-made institution, especially to politicians, judges, bureaucrats and faceless government agencies. The Second Amendment along with the other nine amendments of the Bill of Rights was designed to prevent individuals' enslavement to government, not just to guarantee people the right to hunt squirrels or sport shoot at targets, nor was it included in the Bill of Rights just to guarantee individuals the right to defend themselves against robbers, rapers and lunatics, or to make sure the states could raise a militia quick, on the cheap to defend against a foreign invader or domestic unrest.
The Second Amendment was designed to ensure that individuals retained the right and means to defend themselves against any illegitimate attempt to do them harm, be it an attempt by a private outlaw or government agents violating their trust under the color of law. The Second Amendment was meant to guarantee individuals the right to protect themselves against government as much as against private bad guys and gangs.
That is why the gun grabbers' assault on firearms is not only, not even primarily an attack merely on the means of self-defense but more fundamentally, the gun grabbers are engaged in a blatant attack on the very legitimacy of self-defense itself. It's not really about the guns; it is about the government's ability to demand submission of the people. Gun control is part and parcel of the ongoing collectivist effort to eviscerate individual sovereignty and replace it with dependence upon and allegiance to the state.
Americans provisionally delegated a limited amount of power over themselves to government, retaining their individual sovereignty in every respect and reserving to themselves the power not delegated to government, most importantly the right and power to abolish or replace any government that becomes destructive of the ends for which it was created. The Bill of Rights, especially the Second and Ninth Amendments, can only be properly understood and rightly interpreted in this context.
Politicians who insist on despoiling the Constitution just a little bit for some greater good (gun control for "collective security") are like a blackguard who lies to an innocent that she can yield to his advances, retain her virtue and risk getting only just a little bit pregnant--a seducer's lie. The people either have the right to own and bear arms, or they don't, and to the extent legislators, judges and bureaucrats disparage that right, they are violating the U.S. Constitution as it was originally conceived, and as it is currently amended. To those who would pretend the Second Amendment doesn't exist or insist it doesn't mean what it says, there is only one legitimate response: "If you don't like the Second Amendment, you may try to repeal it but short of that you may not disparage and usurp it, even a little bit, as long as it remains a part of the Constitution, no exceptions, no conniving revisions, no fabricated judicial balancing acts."
Gun control advocates attempt to avoid the real issue of gun rights--why the Founders felt so strongly about gun rights that they singled them out for special protection in the Bill of Rights--by demanding that individual rights be balanced against a counterfeit collective right to "security" from things that go bump in the night. But, the Bill of Rights was not a Bill of Entitlements that people had a right to demand from government; it was a Bill of Protections against the government itself. The Founders understood that the right to own and bear laws is as fundamental and as essential to maintaining liberty as are the rights of free speech, a free press, freedom of religion and the other protections against government encroachments on liberty delineated in the Bill of Rights.
That is why the most egregious of the fallacious arguments used to justify gun control are designed to short-arm the citizenry (e.g., banning so-called "assault rifles") by restricting the application of the Second Amendment to apply only to arms that do not pose a threat to the government's self-proclaimed monopoly on the use of force. To that end, the gun grabbers first must bamboozle people into believing the Second Amendment does not really protect an individual's right to own and bear firearms.