Kinematic Linkages - Computer Animation: Algorithms and Techniques - page 164

Ball-and-socket joint Planar joint

T 2

3

1

T 1

2

zero-length linkages zero-length linkage

Ball-and-socket joint modeled as 3 one-degree joints
with zero-length links

Planar joint modeled as 2 one-degree
prismatic joints with zero-length links

FIGURE 5.4
Modeling complex joints.

5.1.1 Data structure for hierarchical modeling
Human figures and animals are conveniently modeled as hierarchical linkages. Such linkages can be
represented by a tree structure of nodes connected by arcs . 1 The highest node of the tree is the root note ,
which corresponds to the root object of the hierarchy whose position is known in the global coordinate
system. The position of all other nodes of the hierarchy will be located relative to the root node. A node
fromwhich no arcs extend downward is referred to as a leaf node . “Higher up in the hierarchy” refers to
a node that is closer to the root node. When discussing two nodes of the tree connected by an arc, the one
higher up the hierarchy is referred to as the parent node , and the one farther down the hierarchy is
referred to as the child node .
The mapping between the hierarchy and tree structure relates a node of the tree to information about
the object part (the link) and relates an arc of the tree (the joint) to the transformation to apply to all of

1 The connections between nodes of a tree structure are sometimes referred to as links; however, the robotics literature refers
to the objects between the joints as links. To avoid overloading the term links, arcs is used here to refer to the connections
between nodes in a tree.