Input: blue crank.
It is an external epicyclic gear mechanism of two satellite gears.
Zf/Zs = 2
Zf: tooth number of stationary grey gear.
Zs: tooth number of green gear.
Tooth number of yellow gear is arbitrary.
Points on the green gear crank trace ellipses in general.
Semi-major axis = Rb + Rg
Semi-minor axis = Rb - Rg
Rb: center distance of the grey and green gears
Rg: distance from the point tracing the line to axis of the green gear
The red is an absolutely straight line because Rb = Rg