Human Modeling: Kinematics - Human Motion Simulation: Predictive Dynamics - page 27

The resulting homogeneous transformation matrix of Equation (2.49) is an
important element in developing the DH representation. For any two rigid bodies,
this transformation matrix characterizes the configuration (position and orienta-
tion) of one with respect to the other in terms of the four important parameters
( d ,

, a ). Therefore, if it is possible to expand this result to the representation of
rigid bodies connected in a serial chain, their multiplication will yield a transfor-
mation matrix relating any two links in the chain. We will expand on this issue in
the following section toward establishing a systematic method for the embedding
of coordinate systems.

θ , α

2.9 The kinematic skeleton
In order to establish a systematic method for biomechanically modeling human
anatomy, it is necessary to establish a convention for representing segmental links
and joints. We can represent human anatomy as a sequence of rigid bodies ( links )
connected by joints . Of course, this serial linkage could be an arm, a leg, a finger,
a wrist, or any other functional mechanism. Joints in the human body vary in
shape, function, and form. The complexity offered by each joint must also be
modeled, to the extent possible, to enable a correct simulation of the motion. The
degree by which a model replicates the actual physical model is called the level
of fidelity .
Perhaps the most important element of a joint is its function, which may vary
according to the joint's location and physiology. The physiology becomes impor-
tant when we discuss the loading conditions of a joint. In terms of kinematics, we
shall address the function in terms of the number of DOF associated with its over-
all movement. Muscle action, ligament, and tendon attachments at a joint are also
important and contribute to the function.
For example, consider the elbow joint, which is considered a hinge or one-
DOF rotational joint (e.g., the hinge of a door) because it allows for flexibility
and extension in the sagittal plane as the radius and ulna rotate about the
humerus. We shall represent this joint by a cylinder that rotates about one axis
and has no other motions (i.e., one DOF). Therefore, we can now say that the
elbow is characterized by one DOF and is represented throughout the topic as a
cylindrical rotational joint, also shown in Figure 2.17A .
On the other hand, consider the shoulder complex. The glenohumeral joint
(shoulder joint) is a multi-axial (ball and socket) synovial joint between the head
of the humerus and the glenoid cavity. There is a 4 to 1 incongruence between
the large round head of the humerus and the shallow glenoid cavity. A ring of
fibrocartilage attaches to the margin of the glenoid cavity forming the glenoid
labrum. This serves to form a slightly deeper glenoid fossa for articulation with
the head of the humerus Figure 2.17B .
There are a number of methods that can be used to model this complex joint
( Figure 2.18 ). One such method ( Maurel et al., 1996 ) is to consider the shoulder
girdle (considering bones in pairs) as four joints that can be distinguished as: the