In my household I simply expect everybody to contribute. Of course, that's only according to their abilities, and of course children should have lots of free time left. But there are chores to be done, and some of them are done by the kids. Their sole incentive doing them is that they contribute to the community they live in.
Over the years we have experimented with many different schemes. There were family meetings where we decided who would take over which chores and responsibilities. In the end, all this wound down sooner or later. Now I just ask the younger kids to do something when it needs to be done, and expect the older ones to see themselves some of the things that need to be done. And if this doesn't work, I won't yell at them, but express my disappointment.
I started out to just expect them to do their part when they were very young. I remember explaining to a 3yo that the reason we do not have dessert for dinner is that he and his siblings refused to help me prepare the table – and doing this on my own used up too much of my time to allow for preparing dessert. IME a child of 3 years learns this lesson after not more than two frustrating Sunday dinners and after this will come and help when you ask.
I have made it clear that I do many more things than they do which I do not like to do either, but which need to be done, because our household depends on them being done. And I have made it clear that I expect them to contribute as much a percentage of their abilities as I do. Since my abilities are so much greater, my part in this is much greater, too, and that's OK. But if they would stop contributing, I would do so, too – and they know that this would be disastrous for all of us.
It's not that the way I deal with this problem works absolutely flawlessly. But then I would expect constant conflicts at the border between spare time and duty and as a parent I don't feel like I am allowed to duck the hassle stemming from this tension. So the kids do their share, and while they sometimes openly dislike it, they do not complain about it to me. They are not stupid and know that I can point at my share, which is much bigger than that of all of them combined.