I am trying to understand the concept of the catapult

I have seen many videos on youtube but can’t understand how to build it.

Have you checked out the build instructions for the Herobot Fling?

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Yes, I would highly recommend checking that out, as well as @FRC973 ‘s video on their catapult (you should look this up yourself).

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I have checked it out but I need something more compact, also I have watching FRC973 videos, but I am trying to understand how does gearratio and rubberbands have effect on launching the balls in the goal.

I find the best way of learning is doing. It would be great to build the Herobot and and see how it functions first hand.

Otherwise I look would into non-VEX related mechanisms and see how they function.

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Here is a great video on a choo choo mechanism linkage for a catapult.

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Here’s another video that shows a VRC application of that type of catapult.

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