Interesting – as I re-open the various attached blend files in 2.8 I don’t see any “Object Constraints” listed, although the objects still follow them. The models are behaving correctly, but (see cgCody reply on Feb 14th) I click on “pushrod” and see no object constraints listed.
I’m not at my computer now, but if I recall, I used bone constraints, and one of the bone layers may be hidden. I’m not sure how the bone layers translate to collections in 2.80.
I’ll continue to poke around. The screen shot seemed to show that you had selected “pushrod” as the object. I’ve clicked on every object, and in Pose mode every bone, and I don’t see a single constraint anywhere. But, I also didn’t look for hidden things. It would be great if you could open that up in 2.8 latest-beta and see what I did stupid.
Bingo! I found it. “Bone Constraints” tab visible only in Pose mode and separate from “Object Constraints.”
Dunno why the two types of constraints warrant two entirely different tabs. If you’ve selected an “Armature” and are in “Pose Mode,” the one tab would do and would be much more intuitive. (But we can’t change that now.)