It's wrong.
As you can see, the two wheels always maintain the same orientation as the axieme reference. this is evidently in contrast with the laws that regulate the coupling of the rotisms.
I don't have a solution, but I think I found a reading key, not encouraging at all:
When you have multiple elements dynamically bound, cinematism responds correctly only for those to whom the movement is directly impressed or to those directly bound to them. when the movement is the result of other constraints, dynamic ones are ignored or misinterpreted.
in the case of the mechanism with single wheel and barrel stuck, if you impose rotation to the wheel, everything works regularly (including the disk that rotates as it should). if instead it imposes rotation to the disk, the dynamic bond between wheel and rod is ignored.
if things are actually in this way and this malfunction is not the result of an incorrect use of the dynamic bond function, then inventor is not a tool at the height of its diffusion and its use can be dangerous for the security implications related to these problems.
for a company that chose it as a reference, it is certainly not a beautiful discovery.
the animation constraints in inventor is an app put there just to make scene... probably do not review it since 2013. However, try to go on the autodesk forum under inventor and see if you confirm our impressions: inventor