Blue, orange, green and yellow bars create a pantograph.
Two red pins and blue one are in line.
The blue pin traces a straight line (in green).
Condition for tracing a straight line:
R1/R2 = AE/EF
R1: radius of pink crank
R2: radius of violet crank
Its length L = 2R2 + 2 (R1 + R2)(FE/AF)
The direction of the line depends on angular position between pink and violet cranks at starting position of the mechanism.
For the starting position in this video, the line is horizontal, in line with O1O2.