While searching for ways to improve pullups I have found the following concepts to apply while aiming to up your pullups. It is as follows:

To really improve your pullup does not really need very strong willpower..... but a whole lot of discipline to not do too much

if you can do 1 pullups then why don't you try to do as many set of 1 pullups. do one pullups ,rest for 10 min then do another one.

The bottomline is:Never do it when you are tired. keep as fresh as possible.

And if you can't do a pullup go find a bar and hold it till you can do at least one.

Try it and tell me the result

You could have tried to make it a bit clearer, but I understand what you are getting at. It sounds like a good idea.

Start out by doing 3 - 5 sets of regular push-ups and do as many as you can in each set. The key is to work the muscle until muscle failure. This forces the muscle to become stronger. Rest for only 30 sec. between sets. Then do another 3 - 5 sets with your legs raised onto a chair, as many as you can in each set with 30 sec. rest between sets. Do these at least every other day. It won't be long before you see a change in the amount of push-ups that you are able to do.
Incorporate a exercise routine using weights to strengthen the back. When doing pull-ups the back muscles are very important.

Mike