Motion Graph
Start with the Tree Graph with the strings included as dashed edges. Replace each edge by f_i edges in series (you can create virtual nodes just to acomodate the edges in series), one for each degree of freedom that the joint i allows. The replaced edges carry a twist also related to the movement it allows.
The twits can be constructed by Twist of a Joint, but at the motion graph they should be only refered by a symbol.