Design concept of linear motion axis

Linear motion mechanisms are divided into two categories: precise linear motion mechanisms and approximate linear motion mechanisms.
There are two main design concepts for precise linear motion mechanisms:
One is to use the inversion transformation in geometry to invert the arc path at the end of the connecting rod into a straight line, which can be accomplished by a mechanical invertor;
The other is to limit the path to the intersection of two planes through two non-parallel connecting rod structures.
Approximate linear motion mechanisms achieve a connection with a degree of freedom of 1 through multiple rods, and adjust the length of the rods so that the motion trajectory of a point contains an approximately straight line segment.