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Input: red gear (receiving rotation from the blue motor).
The gear meshes with the blue rack. The gearbox has 4 rollers that roll along a blue runway fixed to the rack and yellow door.
The gearbox is connected to the stationary wall by a pink connecting rod. This arrangement allows the gearbox to be shifted when the door moves laterally.
Yellow door slide on two blue rails. The 45 deg. corners at the rail ends make the door flush with the wall.
This design is used for van sliding doors:
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