The courts have already defined the answers you seek.  Private citizens are permitted to possess the same types of weapons the infantry foot soldier would carry on the battlefield.

Now, to make the case for or against explosives, you have to dig deeper. 
There are weapons of mass destruction, strategic weapons, and tactical weapons.  In most analyses of the types of weapons we as citizens can own, there is one important factor:  what weapons do the people who threaten us possess?
If the mass majority of crimes committed with firearms involve handguns, then we need those.  If a large number use AR-15s or other semi-auto rifles, then we need those (AR is no more effective in overall lethality than a hunting rifle, and it's out-matched in caliber by almost any hunting rifles larger than .223).  If criminals use shotguns, we need those, too.  The 2nd is NOT about hunting and target shooting.  Those are legitimate needs for firearms, but they should never be the center of the debate.
Nukes and rocket launchers?  We should NOT own nukes as individuals -- WMD is never considered a defensive weapon for individual use.  If the threat rises to that level, then someone is pissed at a LOT more people than just me! (I hope!!)
Rocket launchers?  If you lived in Somalia, and the people threatening your life carried those, then I'd say yes (given we had the same Constitutional law there)!  Here in the US?  Not too many RPG attacks in the news, so for now, no need for them, and no need to make them legal to own. See where this is headed?  There is no litmus test or concrete factors that we can apply to the law and thereby make a list of weapons to allow or deny to the individual.  The weapons we should be allowed to own are dictated by the threats we face.  Cops face criminals everyday and need adequate firepower to compete (and hopefully surpass) the firepower of the crooks.
You and I face the same threats as Cops, so we should be allowed at least the same weapons they  justify for their own use.  That includes body armor and greater than 10 rd mags.
The Constitution is not specific for a reason....
Have you ever been in the military?  If so, you're familiar with regulations.  Regulations are written at the JCS and headquarters level in very broad terms.  They outline the scope, purpose, and rationale behind the regs as well as the objectives they intend to meet.  Once the next tier of the military gets that, be it combatant commands or their support units, those organizations IMPLEMENT the regs by doing what you said:  write definitions, assign units responsibilities, identify material and personnel requirements, and so forth.  They do all that to meet the intent of the vague, broad, and general higher-level guidance.
Look at the Constitution as if it is the Joint Chiefs.  It outlines the overall goal of what it sets out to accomplish.  The legislature then enacts more detailed, but still higher-level,federal laws to require the states and individuals to comply with those laws.
The states then write their own laws to implement programs, enforcement units, budgets, training, etc. to stipulate in detail HOW we are going to meet the intent of the federal laws.  When laws are ambiguous, we still have to look at the spirit, and not just the letter, of the law to see if one is in compliance. The only part of the Constitution that lists details, like how old a President must be at a minimum, voting age, and all that are in the amendments, because people saw a need to standardize some requirements instead of letting each state make up their own rules for those specific clauses.
Putting the details of every law in the Constitution to the level needed to implement the laws would be impossible.  Even if we tried, as situations change, the Constitution would need constant ratification to make those changes. 
The founders made it difficult, but not impossible, to change the document for a specific reason.  They knew they were not perfect.  They were wise enough and humble enough to understand they couldn't think of everything.  They hoped future generations would preserve what was working and correct what was not.  This document was so important, they required lawmakers to go though a very difficult process of state ratification and super majority votes before they could change it.
No founder thought about, or cared about, semi-auto firearms or nukes.  They left the details to us.  What they did spell out is that the individual has a right to defend himself and his family from all threats, including a  government run amok.   Remember, they had just finished fighting the most powerful government on the planet over the very issues they included in the Declaration of Independence.   
You have described why these discussions and debates continue ... because people with opposing viewpoints always exist.  The beauty of our government over all others before it is we can voice our dissent and work within the system to effect change without the need to resort to violence.  Look at Egypt and Libya and even Iraq.  It took full-on warfare to topple these dictators.  An election was not going to do that.  We are way ahead of the other forms of gov't just in that one example alone!

I did some searching but have not found any court cases specifically defining the word arms. Are you aware of any specific ones?

I did find this article which appears very well written mentioning a specific case where the court touched on the issue. It is long but does a good job of explaining different ways of analyzing the constitution and specifically the 2nd amendment. Especially interesting is the analyses on different ways of interpreting a law. (as a living document using modern situations vs using historical writings to try and ascertain intent vs simply analyzing the text itself but using other historical documents to understand how words were used at the time) The author prefers what he calls the textual analyses.
In the end the author summarizes with this after mentioning the preamble.

I think the preamble supports the idea that we the people can rein in someone’s claim to a “right” if that right presents enough of a threat to our domestic tranquility, and if the general welfare of our people is in enough danger. The danger posed by powerful weapons controlled by incompetent, careless, or malevolent individuals obviously qualifies."

http://brainshavings.com/the-right-to-keep-and-bear-what/

I think the author lays out a very good basis on how we might decide which arms to allow as well as who to allow them to.
In that line of reasoning I think it makes sense to ban explosive type weapons. Specifically as the author says the right presents enough of a threat to our domestic tranquility, to which I think explosives would apply. RPGs do not make all that great of a self defense tool anyway. (a lot of collateral damage from an explosion, etc)

I do think you did a good job of outlining a reasonable argument and clearly you recognize it is not an easy black or white issue, that a gray area does exist and that certain types of arms can be regulated. My gray area probably lies a little more towards the middle than does yours but we are generally on the same side. Certainly other peoples gray areas lie much father to the left. I am willing to compromise on things that are in my gray area, an example would be fully automatic firearms, that is something I would be willing to bargain away if it meant a stronger guarantee for the protection of firearms below that level. That is just an example I am using to illustrate and I do not mean to get into  debate about the nitty gritty of what regulations are good or bad.

And on a side note I just now saw the graphic posted. For some reason the other computer I was on wasn't displaying the graphic.

Which arms are we Constitutionally allowed to keep and bear?

Aymette v. State, 21Tenn. 154, 156 (1840), In Aymette, the Tennessee Supreme Court construed the guarantee in Tennessee’s 1834 Constitution that “ ‘the free white men of this State, have a right to keep and bear arms for their common defence.’ ” Explaining that the provision was adopted with the same goals as the Federal Constitution’s Second Amendment , the court wrote: “The words ‘bear arms’ … have reference to their military use, and were not employed to mean wearing them about the person as part of the dress. As the object for which the right to keep and bear arms is secured, is of general and public nature, to be exercised by the people in a body, for their common defence, so the arms, the right to keep which is secured, are such as are usually employed in civilized warfare, and that constitute the ordinary military equipment.”

    1. The act of 1837-8, ch. 137, sec. 2, which prohibits any person from wearing any bowie knife, or Arkansas tooth-pick, or other knife or weapon in form, shape or size resembling a bowie knife or Arkansas tooth-pick under his clothes, or concealed about his person, does not conflict with the 26th section of the first article of the bill of rights, securing to the free white citizens the right to keep and bear arms for their common defence.
    2. The arms, the right to keep and bear which is secured by the constitution, are such as are usually employed in civilized warfare, and constitute the ordinary military equipment; the legislature have the power to prohibit the keeping or wearing weapons dangerous to the peace and safety of the citizens, and which are not usual in civilized warfare.
    3. The right to keep and bear arms for the common defense, is a great political right. It respects the citizens on the one hand, and the rulers on the other; and although this right must be inviolably preserved, it does not follow that the legislature is prohibited from passing laws regulating the manner in which these arms may be employed.

Which arms are we Constitutionally allowed to keep and bear?

The arms, the right to keep and bear which is secured by the constitution, are such as are usually employed in civilized warfare, and constitute the ordinary military equipment;

Well, hell, I ain't civilized, but were I going to try to be, guess I'd have to get rid of my flame thrower, anti-personnel mines, and nerve gas.

Darn, those Claymores out on the front lawn were so comforting to have should an alphabet agency to come sniffing around...................................

Which arms are we Constitutionally allowed to keep and bear?

Good thing I am a free white man!

Also it seems that the commentary is saying that arms can be kept but not worn around (CCW). We can have the same civil firearms that the military uses we can be restricted from wearing it.
It is interesting to read old court cases but this one just raise more questions for me. It seems to give us more rights in one area but take rights away in another.
Thanks for posting that!

Good thing I am a free white man!

Also it seems that the commentary is saying that arms can be kept but not worn around (CCW). We can have the same civil firearms that the military uses we can be restricted from wearing it.
It is interesting to read old court cases but this one just raise more questions for me. It seems to give us more rights in one area but take rights away in another.
Thanks for posting that!

Never take one case out of context and in a vacuum.  The specific issue which brings the case before the court (charges filed, rights denied, ...) and the subsequent cases which use this one as precedent, as well as challenges in higher courts, all combine to form the body of law affecting the specific issues raised.

So, this case was not supposed to put to rest all questions about right to bear arms.  it was tried because

an indictment was filed against William Aymette. This indictment charged: 1st. That Aymette on the (p.155)26th day of June, 1839,
in the county of Giles, "did wear a certain bowie knife under his clothes, and keep the same concealed about his person, contrary
to the form of the statute". "That on the same day, the said Aymette did wear a certain other knife and weapon, in form, shape and
size resembling a bowie knife, and under the clothes of him the said Aymette, and concealed about the person of him".

I bet that opens up even more questions for you!   

It's easy to get lost in the "weeds" with the specific details about what is or isn't a legitimate arm/weapon for a law-abiding citizen to own, BUT let's look at the issue of compromise from the actual at-the-moment reality we face in Hawaii. We cannot carry any weapon outside our private property for self-defense that would be effective in anything other than hand to hand combat/assault, and cannot own many such arms/weapons as would be effective at a safer distance than contact even on our property. No guns in public (obviously). No "stun guns" (illegal to possess). No standard capacity manufacturer magazines if they are over 10 rounds. No pepper spray in over 1/2 ounce size. No expandable batons. 14 to 20 day waiting period for handgun permit. Registration of "unusable, unserviceable" firearms. Registration of any firearm owner (never been used to solve a crime). Long gun barrel length of less than 16 inches. Fully automatic or burst fire option. Hearing protection in the form of noise suppressor. Etc. Etc. Etc. This is what I'm talking about when I assert "no compromise". These issues are clear. There is no rational reason, nor any evidence that will withstand critical scrutiny that could possibly support the government rationalization of having "a compelling interest in public safety". Period. No compromise. These are clearly abuses of the natural, civil, fundamental, individual Constitutionally-guaranteed rights of law-abiding citizens. Why would we willingly "compromise" our rights for no legitimate reason?All of these things prohibited (or enforced) in Hawaii are legally allowed (or no registration, etc. to be enforced) in the vast majority of states and local jurisdictions in the Untied States, and there is no abuse by law abiding citizens. And the criminals ignore the laws as they always have.

If we obey these laws we 1. put ourselves, our families and friends, and our communities at greater risk of being victimized by criminals who obviously never have and never will obey any such laws that jeopardize us, and 2. we have submitted to illegitimate authority and allow them to take further and further steps deny our rights and encroach upon our lives in ways no government ought to.

If we disobey these absurd illegitimate laws (by, for instance, carrying a weapon concealed outside our property), we instantly become serious criminal felons, and if caught, even though we have harmed no one, are subjected to severe criminal and civil sanctions.

I don't see where "compromise" is an option worth considering.

Never take one case out of context and in a vacuum.  The specific issue which brings the case before the court (charges filed, rights denied, ...) and the subsequent cases which use this one as precedent, as well as challenges in higher courts, all combine to form the body of law affecting the specific issues raised.

The thing about being a white male was really just a joke...

It's easy to get lost in the "weeds" with the specific details about what is or isn't a legitimate arm/weapon for a law-abiding citizen to own, BUT let's look at the issue of compromise from the actual at-the-moment reality we face in Hawaii. We cannot carry any weapon outside our private property for self-defense that would be effective in anything other than hand to hand combat/assault, and cannot own many such arms/weapons as would be effective at a safer distance than contact even on our property. No guns in public (obviously). No "stun guns" (illegal to possess). No standard capacity manufacturer magazines if they are over 10 rounds. No pepper spray in over 1/2 ounce size. No expandable batons. 14 to 20 day waiting period for handgun permit. Registration of "unusable, unserviceable" firearms. Registration of any firearm owner (never been used to solve a crime). Long gun barrel length of less than 16 inches. Fully automatic or burst fire option. Hearing protection in the form of noise suppressor. Etc. Etc. Etc. This is what I'm talking about when I assert "no compromise". These issues are clear. There is no rational reason, nor any evidence that will withstand critical scrutiny that could possibly support the government rationalization of having "a compelling interest in public safety". Period. No compromise. These are clearly abuses of the natural, civil, fundamental, individual Constitutionally-guaranteed rights of law-abiding citizens. Why would we willingly "compromise" our rights for no legitimate reason?All of these things prohibited (or enforced) in Hawaii are legally allowed (or no registration, etc. to be enforced) in the vast majority of states and local jurisdictions in the Untied States, and there is no abuse by law abiding citizens. And the criminals ignore the laws as they always have.

If we obey these laws we 1. put ourselves, our families and friends, and our communities at greater risk of being victimized by criminals who obviously never have and never will obey any such laws that jeopardize us, and 2. we have submitted to illegitimate authority and allow them to take further and further steps deny our rights and encroach upon our lives in ways no government ought to.

If we disobey these absurd illegitimate laws (by, for instance, carrying a weapon concealed outside our property), we instantly become serious criminal felons, and if caught, even though we have harmed no one, are subjected to severe criminal and civil sanctions.

I don't see where "compromise" is an option worth considering.

I agree, there really isn't much left to compromise in Hawaii. Perhaps though we could trade one thing for another, like get hi cap mags back in exchange for a law could prevent seriously crazy people from owning firearms. (just an example)

Where is it written that people cannot have pepper spray over ½ ounce? I haven't seen that one before.

I was talking to a gas station convenience store worker who explained they had been robbed some time ago. She was surprised when I explained that she can carry a gun at work. Most stores don't want employees to fight suspects though as they don't want to pay for workman's comp claims.