Translational and rotational movement?

Question

Physics

In one book on physics there is such a question:
Is the forward movement of the pedals when riding a bicycle (without free play). In the course of googling, everyone gives the answer that yes, it is progressive.
The definition of translational motion in the book itself: The motion is called translational, in which all points of the body move in the same way, describing the same trajectories.
Let's take a point at the tip of the pedal and another point closer to the axis of rotation, so what is the same trajectory for them?

Answer 1

Translational motion is
a motion in which a straight line drawn in a solid body at any time remains parallel to itself.
Since the pedals move *without free play*, their position at any moment of time is parallel to any other moment of time.
Accordingly, the condition is met
*Let's take a point on the tip of the pedal and another point closer to the axis of rotation, so what is the same trajectory for them?* - try to schematically sketch the movement of the points of the pedals, which retain their parallelism. You will notice that their trajectories are the same (with an offset, but this does not contradict the definition of translational motion)

Answer 2

Translational motion is an example with a piston.
Pedaling is NOT forward movement.
Reading the definition:
If we take the example of pedals, then the parallelism in movement will be broken.
The Internet is often wrong. You need to think with your head.