Linkages can be used to make things move in opposite directions. The movement is reversed by using a lever to form the linkage. If the pivot point (fulcrum) is at the centre of the connecting lever then the output movement will be the same as the input movement but it will act in the opposite direction.
If the pivot point is not in the centre of the connecting lever then the movement of the output will not be equal to the movement of the input. By careful positioning of the fulcrum, it is possible to design a linkage system which moves an exact distance. It is also possible to design the linkage to produce mechanical advantage.