Human Modeling: Kinematics - Human Motion Simulation: Predictive Dynamics - page 25

Therefore, to calculate the final position of the hand, we substitute for values
of q 1 and q 2 , which yields the final position of the hand as
x 5

T

8 : 10 5 : 28 (2.47)

From this simple example, it can be seen that if the number of DOF becomes
large, and the orientation of each joint with respect to another is spatial rather
than planar, the formulation of the x , y , and z equations becomes complicated. If
the orientation of the hand is required, further complexity is introduced.
Therefore, we need to develop a systematic methodology for:

a. Locating coordinate systems on each segmental link in a consistent manner.
b. Calculating the relation between any two segmental links.
c. Characterizing the position and orientation of a distal link on the kinematic
chain with respect to another link on the same or different chain.

2.8 The DenavitHartenberg representation
In order to obtain a systematic method for describing the configuration (position
and orientation) of each pair of consecutive segmental links, a method was pro-
posed by Denavit and Hartenberg (1955) . We shall utilize the method of Denavit
and Hartenberg (DH) to address human kinematics.
The method, now referred to as the DH method, is based upon characterizing
the configuration of link i with respect to link i

4) homogeneous
transformation matrix representing each link's coordinate system. If each pair of
consecutive links represented by their associated coordinate system ( Figure 2.15 )
is related via a matrix, then using the matrix chain-rule multiplication, it is possi-
ble to relate any of the segmental links (e.g., the hand) with respect to any other
segmental link (e.g., the shoulder).

1bya(4

2 3

Z i-1

Z i-1

Z i

Z i

X i-1

X i-1

Y i

FIGURE 2.15
Joint coordinate systems between two segmental links.