Scotch yoke

A Scotch yoke changes a rotating motion into a linear motion. It is an example of a slotted link mechanism. The rotating wheel with an off-centered mounted peg moves the yoke to the left and right. The displacement depends on the size of the slit in the yoke and the position of the peg on the wheel.

This 3D printable model is mainly to illustrate the workings.
For sure, better designs that include sliding and rotation bearings to minimize play and friction can be thought of.

In the model the yoke can be moved by rotating the wheel by hand. Coupling the wheel directly to a motor or using a gear set would provide a controlled linear motion with a changing speed when approaching the maximum extension.

See e.g.: https://en.wikipedia.org/wiki/Scotch_yoke