A cardboard lifting wheel (cam)
A wheel with its turning hole off-center can lift something as it turns. Make one from card and put the movement to use.
Get to know it
Picture a cardboard wheel standing upright on a horizontal wooden rod. A little platform rests on its top edge. If the hole is in the middle, turning the wheel leaves that platform at the same height. Move the hole to one side and the top edge rises and falls, taking the platform with it. That lifting wheel is a cam.
The hand-cranked creature uses a 6 cm cardboard circle with its hole 1 cm away from the center. The wheel is fixed to a turning wooden rod. A little platform rests loosely on its edge. A separate upright rod slides through a straw fixed to the box, keeping the character over the wheel. The project has a model you can turn to see these connections.
You make this part from cardboard, rather than buying a component called a cam. Stiff layered card can serve a light paper character; it is not interchangeable with wood or metal carrying a heavier load. A different hole position or outline can produce another movement, provided the wheel has room to turn and the platform stays in contact.
The same rise and fall could bring a face up behind a curtain, raise a small flag, or lift one end of a loosely hinged paper wing. Those are possibilities to develop, not tested constructions. What you want to move can suggest the next shape and connection.