Hello. I just started constructing. A couple days ago I found "inkscape". Free. You move a sprite into it and tell it to make it mathematical. It does it's best and changes the object to lines and boxes and circles that you can move around, manipulate etc.
say you have a stick-man. You just duplicate it, move the arm line upwards a little and rotate if neccessary, then duplicate again and move a little bit more, then duplicate again... so you have the frames of an animation. BUT...
There is also one neat feature called "interpolation" What you do is you put the first frame, and make the last frame, and choose two frames and say interpolate in x steps. The program makes x frames in-between the two frames you fed it. But you should only use simple sprites for this as complicated sprites are not easy to interpolate.