The locking mechanism for a standard combination padlock consists of three notched discs or cams and a pawl. The process of dialing the correct combination lines up the three notches under the pawl. When the shackle is pulled, the pawl drops into the notches, allowing the shackle to release and the lock to open.

"Carl" has been generous enough to provide us with pictures of disassembled locks.
Click on any picture to see it full size. Use your browser's back button to return. Below is a picture of a disassembled Master combination padlock, viewed from the rear. Two of the cams have been removed. The front cam, which is attached to and directly driven by the dial, is visible. I refer to it as the front cam because it is closest to the front of the lock. The deep notch on the front cam is lined up under the pawl If the shackle were pulled, the latch assembly would pivot, allowing the shackle to be pulled out of the lock.

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How the Combination Lock Works