The differences between these three has to do with what happens when you pull the trigger of the weapon.
In a single action weapon, only one thing happens when you pull the trigger: it releases the hammer or striker to fire the weapon. This mechanism was used by early revolvers, such as the Colt Paterson, Walker Colt, Colt Single Action Army (a.k.a. the Peacemaker) revolver etc. and is still used by many modern rifles, shotguns and semi-automatic pistols.
Colt Single Action Army revolver. Click on the image to enlarge. Public domain image.
To fire a weapon like the example above, the user first cocks the hammer by pulling on the spur at the back of the hammer with the thumb, until it locks into position. Then, when the user pulls the trigger, it releases the hammer, which then falls back down towards the cylinder with considerable force, due to a spring connected to the hammer, and thereby fires the weapon. If the hammer is already down, then pulling the trigger does nothing. To fire another round with this revolver, the user needs to re-cock the hammer back again before pulling the trigger. The key thing to note with single actions is that if the hammer (or striker) is down, then pulling the trigger does nothing.
The above video from hickok45 shows a Colt single action revolver being used. Notice how he pulls back the hammer before every shot, to cock it. Also note that the act of pulling back the hammer also rotates the cylinder to bring the next cartridge under the hammer. The user cannot fire this weapon by only pulling on the trigger.
Some semi-automatic pistols like the Colt M1911 and Springfield XD are also single action weapons. The Colt M1911 is hammer fired and the Springfield XD is striker fired, but they are both single action.
Most modern rifles and shotguns are also single action.
Since the weapon is already cocked, the trigger pull force required to discharge it is typically small and a force of around 3 to 4.5 lbs. (about 1.3 - 2 kg.) is enough to release the hammer or striker.
With a Double Action Only (DAO) weapon, pulling the trigger does two things: it first pulls the hammer (or striker) back to cock it and then pulling the trigger further releases the hammer or striker. Therefore, two actions happen on the same trigger pull, which is why it is called double action. The force required to operate the trigger is much higher than single action weapons, typically about 10 to 12 lbs. (about 4.5 to 5.5 kg.). This is because the trigger has to cock the hammer or striker against spring pressure and more force is required to do this.
The first example of a double action only weapon was the Adams revolver invented in 1851.
An Adams revolver. Click on the image to enlarge.
Note that the Adams revolver has no spur on the hammer, therefore the user cannot pull it back with the thumb. The good news is that the missing spur means that it cannot get snagged by accident on anything and it is also possible to fire this revolver much faster than the Colt single action revolver, since there is no need to cock it each time before pulling the trigger. The bad news is that the trigger is harder to pull and due to the larger force needed, there is a tendency to shake the revolver when pulling the trigger, which makes it less accurate.
Some modern day semi-automatic weapons and revolvers still use a DAO action, Examples include the SIG P250 pistol, the Ruger SP101 revolver, the Taurus 24/7 pistol, Smith & Wesson Bodyguard revolver etc.
Notice how there is no spur at the back of this revolver, so the only way to cock this weapon is to pull the trigger. At around 1:00 of the video, you can clearly see the hammer being moved backwards initially as the trigger is being pulled and then released as the trigger is pulled further along.
From all the above, we see that double action weapons only need one trigger pull to both cock and fire the weapon, thereby being faster to fire, but they need more pull force on the trigger than single action weapons, which leads to the weapon shaking more when the trigger is pulled. Therefore, there is another alternative, which combines the best of both: the double action/single action also known as DA/SA, single action/double action or SA/DA.
With a double action/single action firearm, it can be fired in both modes. One of the first examples of this was the Beaumont-Adams revolver, which was invented in 1865 by Lieutenant Fredrick Beaumont of the British Army. He was a veteran of the Crimean war and had used the Double Action Only Adams revolver there. After the war, he decided he was going to improve the Adams design and invented his revolver.
A Beaumont-Adams reovlver Click on the image to enlarge. Public domain image.
With this design, the user has two options. When the hammer is down, the user can pull the trigger, which cocks the hammer and then releases it, just like a double action only revolver. Doing this takes more trigger pull force, as expected. The user also has the option to cock the hammer by pulling the spur at the back of the hammer, just like a single action weapon. In this case, there is less force required to pull the trigger, as the hammer is already cocked,
A DA/SA weapon combines the best features of both the single action and the double action weapons and gives the user a choice of which mode to fire the weapon with. Some modern weapons that use this system include the Beretta M9 pistol, which is the standard sidearm of the US military, the Colt Python revolver, SIG Sauer P-220 pistol, the Heckler & Koch USP pistol, the Czech CZ 75 pistol etc.
Heckler & Koch USP pistol. Click on the image to enlarge.
Image licensed under the Creative Commons Attribution-Share Alike 3.0 license by Miroslav Pragl
When the trigger is pulled with the hammer down, it requires a force of something like 10.5 lbs (4.5 kg.) to discharge the firearm, but if the hammer is already cocked, it requires a force of only about 4.5 lbs (2 kg.) to do it.
With a semi-automatic weapon like the pistol above, if the weapon is not cocked after the magazine is loaded, the first trigger pull will be heavier, since it has to cock the weapon first. But after the first cartridge is fired, the weapon uses some of the recoil force to cock itself automatically, which means the subsequent trigger pulls do not require as much force. The user can also cock the hammer manually using the thumb to pull it back, or cock it by pulling back on the slide, in which case the first trigger pull will be lighter since the weapon is already cocked. Many pistols also have a de-cocking lever to safely lower the hammer back down to double-action mode.
Some people like to carry the weapon de-cocked, because the first trigger pull needs much more force and therefore, it is less likely to be pulled accidentally when the user is carrying the weapon in a holster. Other people find the fact that the first pull needs more force than the others a little confusing, so they carry the weapon cocked and enable the weapon safety devices instead.
Finally, we have some weapons that cannot be exactly classified as either double-action or single-action. Examples of this would be Glock and Kahr pistols. As we saw in our previous post, which showed an animated image of a Glock pistol in action, when the slide is pulled back, it pulls the striker back and locks it at an intermediate position where the spring is only at partial tension. Pulling on the trigger pulls the striker back first (so the spring reaches full tension) before releasing the striker, much like a double action weapon does. However, unlike a double action weapon, if the striker is not cocked at the intermediate position first, pulling on the trigger does nothing (behaving exactly like a single action weapon).
A Glock 17 pistol. Click on the image to enlarge.
As you have probably already guessed, the trigger pull force for a weapon like this is between that needed for a single action and a double action weapon. For instance, a standard Glock trigger requires about 5.5 lbs (2.5 kg.) to operate it and a Smith & Wesson M&P needs about 6.5 lbs (2.95 kg.).
The video below contains some good examples that show the differences between the various mechanisms: