User guide

Charnwood Dynamics Ltd. Coda cx1 User Guide – Advanced Topics III - 4
CX1 USER GUIDE - COMPLETE.doc 26/04/04 112/162
Knee and Hip Moments
The analyses for the knee-moments on the shank and the hip-moments on the thigh are
essentially the same as for the ankle-moments except that the ground reaction vector is
replaced by the distal joint reaction and we must include an extra term to account for the
distal reactive moment.
Thus, for the knee moment:
Centre of mass of shank: G
S
= K + µ
S
(A - K)
Linear acceleration of centre of mass of shank: a
G
s
= a
K
+ µ
S
(a
A
- a
K
)
Ankle joint forces: R
K
x
= m
s
a
G
sx
- R
A
x
; R
K
y
= m
s
a
G
sy
- R
A
y
R
K
z
= m
s
(a
G
sz
+ g) - R
A
z
Torque due to knee force:
s
Q
R
K
= R
K ^
d
K
where d
K
= K - G
S
Torque due to ankle force:
s
Q
R
A
=
R
A ^
d
A
where d
A
= A - G
F
Torque due to ankle moment:
s
Q
M
A
=
M
A
(ankle moment vector with components
relocalized into EVB of the shank)
Total torque on shank: Q
s
=
s
Q
R
K
+
s
Q
R
A
+
s
Q
M
A
= [ Q
s
x
, Q
s
y
, Q
s
z
]
T
Localization:
shank
Q
0
= Q
s
.
shank
e
0
,
shank
Q
1
= Q
s
.
shank
e
1
,
shank
Q
2
= Q
s
.
shank
e
2
Then
M
K 0
=
shank
I
0
shank
α
0
+ (
shank
I
2
-
shank
I
1
)
shank
ω
1
shank
ω
2
+
shank
Q
0
M
K 1
=
shank
I
1
shank
α
1
+ (
shank
I
0
-
shank
I
2
)
shank
ω
0
shank
ω
2
+
shank
Q
1
M
K 2
=
shank
I
2
shank
α
2
+ (
shank
I
1
-
shank
I
0
)
shank
ω
1
shank
ω
0
+
shank
Q
2
The moments at the hip are obtained with an identical analysis by simply replacing all
sub/superscript references as follows:
shank (S) --> thigh (Th)
knee (K) --> hip (H)
ankle (A) --> knee (K)
It is worth bearing in mind that in the formulae for the Euler Equations above, the middle
terms involving products of segment angular velocities and differences of inertia will have
only a very minor contribution to the moments.