Biomedical Engineering Reference
In-Depth Information
3.7.1
Joint displacement
The neutral position q
N
represents a relatively comfortable position. Consider
q
i
as the neutral position of a joint measured from the home configuration, which
is characterized by q
5
0. Then, conceptually, the displacement from the neutral
position for a particular joint is given by
j
q
i
2
q
i
j
. However, to avoid numerical
2
are used. Each of these
terms (one for each DOF) serves as an individual objective function. The terms
are combined using a weighted sum. The scalar weights w
i
are used to stress the
importance of particular joints. The consequent joint displacement function is
given as follows:
ð
q
i
2
q
i
difficulties and non-differentiability, the terms
Þ
X
DOF
w
i
ð
q
i
2
q
i
2
f
Joint displacement
ð
q
Þ
5
Þ
(3.7)
i
5
1
We have determined the values for the weights based on trial-and-error experi-
mentation with the 21-DOF model, and they are given in
Table 3.2
.
For this model, the neutral position is chosen based on observation of the
skinned model in the previous chapter (see Figure 2.25) rather than a skeletal
model. The resulting vector q
N
is defined as
q
i
5
0
;
i
1
; ...;
12
;
19
;
20
5
q
13
52
q
14
5
q
15
5
q
16
52
q
17
52
15
:
0
;
20
:
0
;
100
:
0
;
10
:
0
;
80
:
0
;
(3.8)
q
18
52
q
21
5
35
:
0
;
15
:
0
This generally represents a posture with the arms straight down, parallel to the
torso. It is known that the human's position gravitates towards the neutral position.
3.7.2
Effort
Effort is measured as the cumulative displacement of the joints from their initial
position, rather than from the neutral position. While discomfort is measured
Table 3.2
Joint Weights for Joint Displacement
Joint Variables
Joint Weight
q
1
; q
4
; q
7
; q
10
100
100 when q
i
2
q
i
.
0
1000 when q
i
2
q
i
,
0
q
2
; q
5
; q
8
; q
11
q
3
; q
6
; q
9
; q
12
5
q
13
75
q
14
; q
15
; q
16
1
50 when q
i
2
q
i
.
0
1 when q
i
2
q
i
,
0
q
17
q
18
; q
19
; q
20
; q
21
1
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