Biomedical Engineering Reference
In-Depth Information
Euler Angles
The coordinates of a body in one orthogonal coordinate system may be related to another
orthogonal coordinate system via Euler angle transformation matrices. For example, one
coordinate system might correspond to markers placed on the patient's pelvis, and the
other coordinate system might correspond to the patient's thigh. The two coordinate sys-
tems are related by a series of rotations about each original axis in turn. Figure 4.9 shows
z
z'
θ
y
x
θ
y
x'
z'
z''
θ
x
y''
θ
x
y'
y'''
θ
z
y''
θ
z
x'''
x''
FIGURE 4.9
The unprimed coordinate system
xyz
undergoes three rotations: about the
y
-axis (top), about the
x
000
y
000
z
000
for a
x
-axis (middle), and about the
z
-axis (bottom), yielding the new triple-primed coordinate system
y-x-z
rotation sequence.
