First consider the simplest case in which there is a 2D tree of links
for which every link has only two points at which revolute
joints may be attached. This corresponds to
Figure 3.21a. A single link is designated as the *root*,
, of the tree. To determine the transformation of a
body,
, in the tree, the tools from Section 3.3.1
are directly applied to the chain of bodies that connects
to
while ignoring all other bodies. Each link contributes a
to the total degrees of freedom of the tree. This case
seems quite straightforward; unfortunately, it is not this easy in
general.

Steven M LaValle 2012-04-20