Look at this article! And this one! I found these articles that details some of the animation techniques that predates digital. Using visual effects to trick the mind of the view and make them think they are seeing something smooth or animated is the base concept of most animations.
Read about how these contraptions work
here!
Joseph Plateau is the mathematician whose discovers are used to develop and support the workings of the phenakistoscope. Read more about that
here
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