Creative mechanical devices can demonstrate abstract facts in a most memorable way.

Paraphrasing John von Neumann, math is not understood, but we get used to it. That seems sadly true for some aspects of math, but we should not let this quote become a justification for not looking for better ways to internalize and explain mathematical concepts.

One such way that has always been particularly appealing to myself are mechanical devices that make abstract processes visible.

The Bean Machine—pebbles into bins

The bean machine or Galton machine illustrates the Binomial distribution in a very hands-on way. Watch the video on Wikipedia; that says more than any explanation I could give here.