Black planar trajectory traced by the violet point can be copied with reducing ratio to other place thanks to a system of two pantograph mechanisms. They are connected together through violet pin and pink bar.
Each point of the pink bar gives reducing copies of the black trajectory (green curves).
Length of blue and violet bars: a + b. Here b = 2a
Length of green bars: a
Length of yellow bars: b
Reducing copy ratio: i = a/(a+b) = 1/3
Length of pink bar: y
Distance between two fixed pivots of the blue bars: z
Condition to get pink bar translate: y/z = b/(a+b)