There will first be an explanation on each arm type from VEX, which will be followed by a Robotics Team member's opinions and tips on using the arm.
"Single swing arm is perhaps the easiest arm to assemble. This is the type of arm which is found on the Cortex ClawBot build. The manipulator on the end follows the arc of the swing arm motion and this could be an issue with a passive fork. scoop, or game piece which needs to remain level. However, it is possible for a swing arm design to pass over the top of the tower and reach the other side of the robot." - VEX
It is true that Single swing arms are the easiest to assemble and it is good for beginners. But it is not recommended for competing. This is because it is very inefficient in scoring for most games. The swing arm is not the strongest structure and also requires a lot of motor power for little movement. It is also important to keep in mind that if the arm swing backwards for more than 90 degrees, it could result in the robot tipping, deeming it unusable for the rest of the match. When a claw is put on the arm, it is also unparalleled to the ground, which makes it hard to manipulate objects.
"The 4-bar arm is a linkage arm and is usually the easiest type of linkage arm to assemble. They consist of a tower connection, a set of parallel linkage arms, and an end tower/manipulator connection. An example of the 4-bar arm can be found on the V5 builds, the V5 ClawBot and the V5 Lift." - VEX
The 4- bar arm is one of the most common arms used in robots. The 4-Bar mechanism can be used not only in arms but in any mechanism as well. The reason why this is common is because it is the easiest linkage arm to assemble, as said by VEX. This is important as a parallel linkage arm helps with manipulating objects.
When you grab a mug, the mug is always parallel to the ground, right? If it wasn't the drink inside will spill. The same logic applies here as well. An arm that makes the end of the manipulator parallel to the ground is more effective than one that is not.
A concern to keep in mind is that the joints of 4-bar arms always have to be a little loose to allow for movement and minimal friction.
"The 6-bar arm is an extension of the 4-bar linkage arm. This is accomplished by using a longer top bar and an extended end bar on the first set of linkages. The longer bar serves as the bottom linkage for the second set of linkages and extended end bar serves as a “tower” for the top two remaining linkages.
A 6-bar arm usually can reach higher than a 4-bar arm, however they extend out farther as they swing up and can cause the robot to tip over if the wheelbase is not large enough." - VEX
The 6-Bar arm is similar to a 4-Bar arm as it is just an extended version of it to reach higher or further objects. There is another concern to the 6-Bar which is that it usually causes more friction than a 4-Bar. This is because there are many more joints than the 4-Bar and each joint causes more and more friction.
"The chain-bar arm uses sprockets and chain to create a linkage arm. This assembly uses a Round Hole insert in a High Strength Sprocket. This sprocket is mounted to the tower and the driving shaft is passed through the tower and insert. The Round Hole inset allows the arm’s shaft to freespin. The shaft is fixed to the arm and a motor with a High Strength Sprocket/Chain system or High Strength Gear system is used to raise and lower it.
Another free spinning shaft is passed through the other end of the arm. The end manipulator is mounted to a second same-size High Strength Sprocket with a metal Square Insert. This insert is used to fix the sprocket to the second shaft. When chain is connected between the sprockets of the arm, the chain acts like a 4-bar linkage as a motor system rotates the arm.
Chain-bar arms are usually assembled as pairs to equalize the forces on the arms.
The advantage of a chain-bar arm is it does not have two linkages coming together limiting its height, however if the chain becomes unsnapped or has a link break, the arm will fail." - VEX
The Chain-Bar arm is another parallel linkage arm but it is less common than a 4-Bar arm or a 6-Bar arm. This is because the chains are made of plastic and can quickly snap if there is too much pressure given to it. So it is important to have enough motor power for a Chain-Bar arm and to make sure that the weight above the arm is not too heavy. It is also important to keep in mind not to make the chains too tight or loose.
"The double reverse 4-bar arm requires the most planning and time to assemble. They are nearly always assembled as pairs to equalize the forces on the arms. The assembly of these arms starts with a four bar linkage. The end linkage serves as a second tower for a top set of four bars.
Typically an 84T High Strength Gear is mounted to the far end of the top linkage of the bottom 4-bar and another 84T Gear is mounted to the near end of the bottom linkage of the top 4-bar. As the arm is lifted the two gears intermesh moving the top set of 4-bars in the reverse direction to the bottom set, extending the arm up.
When designing a double reverse 4-bar arm it is important to provide clearance so the top 4-bar can pass either to the inside or to the outside of the bottom 4-bar. Providing as many cross supports as possible between the pair of arms will help keep the arms stable.
Many double reverse 4-bar designs mount the lift motor(s) with a 12T gear to the second tower and drive the 84T gears on the lift. Although, they can be lifted with motor(s)/gear systems on the stationary towers attached to the chassis or both locations.
Double reverse 4-bars can have the highest reach of all the arms discussed. Due to the possible extreme height which can be reached with this design, caution needs to be used when driving the robot with the arm fully extended or the robot may tip over." - VEX
This arm is the hardest to build and even experienced people have a hard time building and maintaining this arm. The two intermeshing gears will grind each other away if you are not careful, so if the gears start to make weird sounds when spinning, the arm has to be stopped immediately. Most people use the DR4B as a lift and not as an arm as it could reach very high when done with long bars. The DR4B always requires at least 2 motors for stability and power and rubber bands needs to be used to maintain the height.
More information about that can be found here.
Depending on the circumstance, choose which factor is most important to you. It is also to keep in mind that there are many other factors which could affect which arm you would use depending on the game.