Barrel Cam Reverser

Yellow pin of the pink slider moves along helical grooves of inside cam shaft (in blue) and outside cam shaft (in glass).
The slider moves along a fixed runway.
Each helical groove consists of right-hand and left-hand portions.
At start position the yellow pin is set to be in opposite hand potions of two grooves. The shafts rotate in opposite directions.
The input is outside cam shaft.
Weakness of this mechanism: unstable positions when the pin is at the corners of each groove. The output inertia helps to overcome them. So at start position the yellow pin must not be at such unstable positions. Adding a device to avoid that is necessary.

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