Rigid or soft body dummy legs? I have a little floating robot character, it's just a sphere with an eye and 4 little "nub" sort of feet legs that extend from it's bottom. I want to do keyframe animation on the sphere, and have the little legs swing and bounce around (within limits on their movement), while attached to the sphere. 

I have some limit rotation constraints set up on them but I decided I want to just simulate them like a puppet's feet or something, instead of manually animating them. How can I achieve this? The sphere is not yet rigged and neither are the legs, will I need to rig them to do this? Or can I handle the little feet with physics and constraints alone? 

I've tried rigid and soft body and setting their parent empty as a constraint target but the feet just fall down infinitely when I bake the simulation. I've never tried to do simulations so I'm not sure where I should be looking to do this. Also at the base of my little feet I have a small colored ring from which they extend, this is animated using a lattice so that when the feet move, this little "rubbery" part deforms a bit as well, and if possible I'd like to preserve that in any simulation, though it's not that important and I could do without it. I should note that I've done a simple character similar to this before but that was without needing any physics.
I think you mean you want the children objects (i.e. the legs) to follow the parent in a delayed way like this:



To do so:


Parent the feet to the body.
Under Relations Extras in the Object Settings, check the Slow Parent checkbox and set the Offset to 10.0


This next step is optional, but if you want to prevent the feet from ever getting farther than a few units away from the body, you can add a Limit Distance constraint. Go to the constraints tab, add a Limit Distance constraint, set the distance to something around 4.0 units and set the target to the parent object: