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Black planar trajectory traced by the middle point of orange bar can be transferred to other place thanks to a system of two pantograph mechanisms.

Orange and pink bars that connect the two pantographs translate.

Each point of the orange bar reproduces the black trajectory (orange curve) thus the multiplying is possible.

Each point of the pink bar gives reducing copies of the black trajectory (green and violet curve).

Length of blue bars: a + b. Here b = 2a

Length of green bars: a

Length of yellow bars: b

Reducing copy ratio: i = a(a+b). Here i = 1/3

Length of orange bar: x

Length of pink bar: y

Distance between two fixed pivots of the blue bars: z

Condition to get orange and pink bars translate: (y-x)(z-x) = b(a+b)

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