I'm working on a Cocos2d-x game and I'm developing on Windows. What I want is to make some skeletal animations, without using a tool or extra software to do so?
Well, the way to go about that is to take a hard look at your linear algebra and go to work. A bone in skeletal animation is just a vector that has another vector as origin and is dependent on its parents scale and rotation. Example skeletal structure:
If you think of all these bones as a relative vector, you can arrange them in a hierarchy, one being dependent on its parent bone.
At the point of every vector, you add an image that is relative to it's position, rotation and scales with the scale of each bone.
Once you've gone through the grueling process of making your hierarchy work correctly with scaling, rotation, etc., you can just keep adding nodes and move them / rotate them over time as you please.
The part of merely rotating, moving and scaling them as you please of course is much harder to get looking good then doing in-editor but hey, here we are. It's a lot harder than doing it with additional software however and I highly recommend an application like Spriter or the like for any skeletal animation.