Bar Pantograph

ABCD: parallelogram
OCE: straight line
O: immobile
OE/OC = BE/BD = k = constant
Figures traced by pointer E and pin C are similar. Scale factor is k.
This is the case when the red tool is immobile (not installed in place of pin C) and the orange pantograph is connected to a system of two sliders (by pin C and a hole of the green plate). The tool traces pink figure on the upper slider. It has same size with the figure traced by pin C but upside down each other.
Instead of system of two sliders an other one can be used, provided that it enables the green plate to move translationally.
Several workpieces can be machined at the same time when many tool spindles are arranged.