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Movables fall into four basic categories: pull tabs, wheels, parallel folds, and angle folds. Flaps, pull tabs and wheels require the user to manipulate a tab, lever, or wheel to see the animated action. Parallel folds and angle folds are page-action pop-ups which move with the opening of the folded page, and require no additional user effort. Understanding these broad categories of mechanisms enable paper engineers to select the right structure for their designs.

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A diagram of the taxonomy of paper mechanisms
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The following models are based on the models presented in The Elements of Pop-Up by James Diaz and David A. Carter.
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Pull Tabs

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Wheels

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Parallel Folds

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Angle Folds

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