Think of your ragdoll character as a tree structure. Each limb has a series of children. When a limb gets moved, all its children are moved with it. The limbs are also affected separately by gravity. This can be done recursively, whereby on drawing each limb, you translate the view matrix by the transformation matrix of the limb, draw it, then call the same function for each child object.

As always, I recommend you know a bit about matrix and vector maths. This is yet another discipline made simpler with matrices.