Some light hints that may point you in the right direction:
Hint 1
The assembly is a part of a larger machine.
Hint 2
Several assemblies are meant to move side by side in unison.
Hint 3
The square-ish shaped piece is plastic that will wear down and be replaced.
Lifter assembly?
The right side clamps onto a bar and the left side rides on a cam and lifts the bar when the line passes under?
Other comment guessed the same thing. The bar controls where the assembly goes instead.