Between my children and children I've cared for, I've found myself in this type of situation many times. If I command they do something, they might do it. If I start doing it and ask them to join me they're a little more likely to. If I do it, willingly and joyfully, because I want it done, because I will feel better when it is done, and my children witness this, then they will not only join when requested, but will often just jump in, or ask me if they can or if I'd like them to. Sometimes all it takes is saying, "hey, let's do [insert task] together. I'll start." They don't feel as though they are my little servants, as though I am a tyrant dictating they do the undesirable work so that I will not have to suffer the drudgery of it. They don't feel like I'm valuing my own preferences and desires over theirs, and trying to force them to accommodate me. I might have to willingly, joyfully do it myself multiple times before they jump in, but generally, they will. I try to remember to be willing and cheerful about the tasks that are generally seen as "mine" too, as my attitude directly teaches them how they should approach "their" tasks. If I can't be willing and cheerful about it, and it's not a matter of extreme importance (life, death, or a dirty diaper), than I do something else until I can again appreciate that task. Most of the time, I don't see much point in grumbling about things that "have to" be done, like changing dirty diapers. Diaper time is belly button raspberries and toe tickling time. 

The younger your child is when you adopt this approach, the easier it will likely be to adjust. You must give your child ample opportunity to be social, to participate in accepted, valued activities that encourage development, even when it's not convenient, not the task you wanted them to do or they are not yet able to do it to the same extent you are. It is essential that you do not hover while they do these tasks, as it would likely give them the impression that you do not believe them capable of these things. Do something else, nearby, keeping busy and watching only peripherally if you feel supervision is necessary.

If your children are older, it may take longer for them to start willingly participating, unasked. Any change in discipline is going to require an adjustment period, (sometimes much longer than we'd like), dedication, and a belief that you are doing something beneficial for yourself, your children, and society in general. Children are often resistant to change. They may test you in unexpected ways. They may simply refuse your invitations to join in tasks for a long time, or they may ask "you're not going to make me do it?" They may ask, "what do I get if I help you." My response would be, "I can't make you do anything. It's your choice," then whistle my way through the task at hand; or for requests for rewards, a smile and "I'll take care of it," or should suffice. I don't know about you, but my head is always full of ideas and thoughts that could use more sorting, and what better than some repetitive, mundane, but useful, task to give me time to meditate on them?

This might all seem blissfully, ignorantly, optimistic. No, it isn't always easy, but neither is screaming, threatening, punishing, arguing, or bribing.

I suggest that you evaluate your own reactions to events, and attitude toward tasks. See if you can identify any of the same behaviors and attitudes that are frustrating you in your children. Ask why you resent or dislike the task at hand, why you are reluctant to do it. Could it be that you were never given the chance to do it just because you wanted to? That you were never given the opportunity to grow up in an environment of obvious unconditional love and acceptance, whether or not you did your chores. That you feel like these are things you have to do, rather than things you choose to do? Could it be that it was taught to you, probably unintentionally, that these are tasks that 'normal,' socially accepted people grumble about and try to avoid, pawn off on others, or do only because there is no way around it? Do you complain about your job or about all the work you do around the house, or about how hard it is to do anything with your crew of wild children, your uncooperative rebels? Do you then expect them to do differently, to go to "work" (school, tasks, etc) willingly, without complaint, and to be anything other than the whiny, wild, uncooperative rebels you've labeled them?