Controlling rotation and translation of an object 4a

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Input: the blue rod with a revolution joint with the green inner tube.
Output: green inner tube performing the following movement: Translate – 180 degree rotate - Rotate backward - Translate backward.
The red pin, fixed to the green tube, moves along a L-shaped slot of the white stationary tube. The slot has a helical portion of small lead angle.
A disadvantage of this mechanism: when the green tube is rotated, it has to translate a bit.
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not sure what drives the rotation of the green cylinder, if the cutout is at 90 degree

morkovija