Considerations for Center of Mass

Post date: Dec 16, 2018 10:31:13 PM

Why is Center of Gravity Important?

Center of Gravity is a vital aspect to consider when designing the robot. Without knowing where it is or what it is, your robot may be toppled over for the duration of the match or in our case, in the game of Rover Ruckus, you may not be able to hang on the lander. It is important to always consider where the center of gravity is so that these problems don’t repeatedly occur. Center of gravity or center of mass(when looked at in 3D) is the average location for the weight of the mass. When looking at the center of mass and gravity an important aspect to consider is stability and how to make the robot stable.

What is and How to Calculate Center of Gravity.

As seen by the equation below, center of gravity can be calculated by knowing the mass of opposite ends of the object. It can also be said that it is the balance point, or where the object can rotate freely about its center of mass. An example of the center of mass concept being used is when you balance a pencil on your finger. When moving it to find the balance point, you are using the equation above to find the point where the pencil will balance, or the center of mass.

The equation above is used for calculating in 2D, but for robotics, since it is in 3D, it is necessary to look at the X, Y, and Z axis. This can be done with the equation below. Though this may look complicated at first, all this is depicting is the sum of the masses multiplied by the distances in the X, Y, or Z axis. This is very similar to the 2D equation but now it is showing it in 3D. This is the important equation to use when looking at the center of mass in robotics.

There are many ways of calculating center of gravity, and they are much easier that it may seem. The first way is to use the equation above. This may be very tough for robots because it is hard to find the mass of the two sides. If it is easier though, this would be the easiest way to find it. Also, for the more veteran teams, using the robot design software PTC, there is a feature which will calculate the center of gravity for you. This though is much more complex since the full robot has to be designed on PTC before the center of gravity can be figured out. The third way which has its flaws is guess and checking. To find the approximate value of the center of gravity, a guess and check method may be done to calculate where this point would be. Though this may seem easy, it may take a long time to find that point since you are initially just making guesses on where it would be. No matter which way you try it is is VERY important to find that point, and it will serve you well for any competition you go to.

Stability of a Robot.

For a robot, it is vital for it to have a proper center of mass because every object whether it is a robot or not, will tend to fall towards its unbalanced side. To make sure that the robot stays stable, it is important to have the center of mass inside the robot. This ensures that the robot won’t tip over since the center of mass is outside the robot. Also, with that it is always better to have the center of mass lower and closer to the robot. Even if the center of mass may be in the robot, if it is high/closer to the side with more weight, the robot has a very high chance to topple over. An example of this can be seen in a remote control car vs. a car in real life. Due to the center of mass being low for the remote control car, it is able to turn more easily than a car in real life which would have a much higher center of gravity than the toy car.

It is important to note that when looking at the same chassis, the position and size of the wheel do make a difference on how stable the robot will be. If looking at a robot with the same frame, and larger wheels, then it would be less stable than a robot with smaller wheels. This is due to the distance between the wheels. Since with larger wheels the distance is smaller, the center of mass would not be in a favorable location and because of this there won’t be the stability in the robot. When looking at the smaller wheels, since there is the distance between the wheels, the center of mass would be closer to the middle giving the robot its stability. The picture below shows the comparison between using larger or smaller wheels on the SAME chassis. If though all larger wheels are used, Ex. the Andymark Mecanum Wheels, it is important to keep them at a far enough distance that the robot will stay stable.

With this being said though, the position of the wheels also makes a huge difference for the stability. As seen with the picture below, with comparing the triangle formations of the wheel vs. a square or rectangle formation, using the same logic as above, the triangle setup, which would give less distance between the wheels, would be less stable than the rectangle setup which if calculated, would have the center of gravity close to the middle of the robot. Note that in these situations the wheels are all the same sizes, and that is kept constant in this scenario.

Not only is it important what types of wheels are used to keep the robot stable, but also if different sized wheels are used, then the question would become where should the center of gravity be located so that the robot stays upfront. This can be answered very simply. Since in many cases the larger wheels go in the back, the center of mass should clearly not be in the back due to the possibility that the robot would fall since it’s heavier in the back. Due to this, it would be much better to position the center of mass closer to the front wheels which, if using the TETRIX set, would be closer to the omni wheels. This would ensure a much lower chance for tipping since there is more weight in the front which would be the less weighted side.

Common Problems for this Game with Center of Mass

There may be very common problems that may occur due to the moving parts of the robot. Though the moving part cause problems, something initially, which caused us serious problems, was from the robot hooking on the lander. Due to the fact that we had more weight on one side of the robot than the other, the robot, as explained above, tended to shift towards that side with the larger mass. This caused that side to be under the two gold blocks, and to our dismay, we were not able to hang. Though we were able to fix this after the meet, this is a problem to look out for, and it is important to fix the center of gravity of the arm to ensure that the weight does not shift to one side. With also this, when using the mecanum wheels, if the center of mass is not in the center of the robot, then when the driver tries to move sideways, instead of doing that action of moving sideway, the robot would rotate. This was also a very serious problem that occurred to us in our last competition. As stated before, this problem is for people who use mecanum wheels for their robot.

Another problem may be that since initially everything is in the inside, the robot would have an initial mass. When the game begins and the robot expands, that would change that initial center of mass to something else. It should always be noted that this center of mass will change and when building the robot it should be noted that the center of mass should be in the boundaries of the robot.

Sources:

• 1. https://www.vexrobotics.com/vexiq/education/iq-curriculum/key-concepts/center-of-gravity