Biomedical Engineering Reference
In-Depth Information
Table 7.1
Link Length and Mass Properties
Link
Length (cm)
Mass (kg)
L
1
8.51
4.48
L
2
38.26
9.54
L
3
39.46
3.74
L
4
5.0
0.5
L
5
9.01
0.7
L
6
7.56
0.23
L
7
9.0
2.32
L
8
5.63
2.32
L
9
5.44
2.32
L
10
6.0
2.32
L
11
17.39
3.0
L
12
16.76
5.78
L
13
20.0
4.22
L
14
17.1
1.03
L
15
4.41
2.8
L
16
25.86
1.9
L
17
24.74
1.34
L
18
16.51
0.5
We shall use these virtual joints to enable generalized global motion of the human
with respect to a fixed coordinate frame at (0, 0, 0).
The two adjacent virtual joints are connected by a virtual link that uses zero
mass and zero inertia to define the link properties. Finally, the virtual joints and
links constitute a virtual branch that contains six global DOFs denoted by (
z
1
,
z
2
,
z
3
,
z
4
,
z
5
,
z
6
).
The virtual joints defined in the virtual branch not only generate global rigid
body movements but also contain global generalized forces. These forces corre-
spond to the six global DOFs:
three forces (
τ
1
,
τ
2
,
τ
3
) and three moments
(
τ
6
). For the system in dynamic equilibrium, these global generalized forces
should be zero.
τ
4
,
τ
5
,
7.4.3
Forward recursive kinematics
We shall use the recursive kinematics and the Lagrangian approaches to carry out
the kinematics and dynamic analyses of the 3D human model. The computational
cost of the recursive formulation is
OðnÞ
. The sensitivity information about a joint
involves only two adjacent joints; therefore, its computational cost is reduced
to
OðnÞ
.
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