Laboratory Experiments:
Measurement and Interpretation of
Muscle Force Vectors, Moments, and
Power for Knee Flexion
Experiments 2 and 3
• Biomechanics of Maximum Isometric
Knee Flexion Torque for Various Knee
Joint Angles
•Biomechanics of Maximum Isokinetic
Knee Flexion Torque for Various Knee
Joint Angles and Angular Velocities
Experiments 2 and 3 – Measured and
Calculated Isometric Parameters
Maximum Isometric (0 deg/sec)
Angle of
Attachment
Knee Joint of Muscle
Muscle
Torque
Joint
Angle
to Shank Muscle
Moment Applied to Turning
(Thata 2) (Theta 1) Length (OI)
Arm
Cybex Arm Force (Fx)
(deg)
(deg)
(m)
(m)
(Nm)
(N)
180
3.41
0.4207
0.00297
165
13.64
0.4185
0.01179
103.14
2062.8
150
30
0.4133
0.025
102.86
2057.2
135
43.5
0.4057
0.0344
101.69
2033.8
120
57.4
0.3953
0.04212
76.06
1521.2
105
71.5
0.3836
0.0474
69.71
1394.2
90
86.2
0.3708
0.0499
64.63
1292.6
Force
Joint
Applied to CompresCybex Arm sion Force
(Fc)
(Fy)
(N)
(N)
Force of
Muscle
Contraction (F1)
(N)
Power
(Nm/sec)
343.8
342.866667
338.966667
253.533333
232.366667
215.433333
7199.31852
4114.39127
2954.63869
1807.78663
1470.1783
1295.44583
0
0
0
0
0
0
6996.21031
3563.16485
2143.25624
976.751287
466.508941
85.8204016
2a. Neatly plot on one sheet of graph
paper Fx versus 2, Fy versus 2, and
F1 versus 2 for maximum
isometric contractions for the knee
joint angles of
165, 150, 135, 120, 105,
and 90. Distinguish between the
three lines.
What interpretation did you make of this
data?
Force vs Knee Angle - Isometric
8000
7000
Fx
Force (N)
6000
Fy
F1
5000
4000
3000
2000
1000
0
180
165
150
135
Knee Angle (deg)
120
105
90
• A relatively small proportion of muscle contraction goes into
turning the joint.
• Most of the force of muscle contraction goes into compressing the
joint, especially when its mechanical advantage is poor.
Force vs Knee Angle - Isometric
8000
7000
Fx
Force (N)
6000
Fy
F1
5000
4000
3000
2000
1000
0
180
165
150
135
Knee Angle (deg)
120
105
90
• When the muscle is at its greatest length (largest knee joint angle),
it exerted substantially greater contractile force.
• The combination of muscle length and mechanical advantage
resulted in a relatively constant turning component (Fx) over the
range of knee joint positions.
Force vs Knee Angle - Isometric
8000
7000
Fx
Force (N)
6000
Fy
F1
5000
4000
3000
2000
1000
0
180
165
150
135
Knee Angle (deg)
120
105
90
Experiments 2 and 3 – Measured and
Calculated Isokinetic Parameters
Maximum Isokinetic (15 deg/sec = 0.2618 rad/sec)
Angle of
Attachme
Knee
nt of
Joint Muscle to
Muscle
Torque
Joint
Angle
Shank
Muscle Moment Applied to Turning
(Thata 2) (Theta 1) Length
Arm
Cybex Force (Fx)
(deg)
(deg) (OI) (m)
(m)
Arm (Nm)
(N)
180
3.41
0.4207
0.00297
165
13.64
0.4185
0.01179
90.17
1803.4
150
30
0.4133
0.025
86.72
1734.4
135
43.5
0.4057
0.0344
80.65
1613
120
57.4
0.3953
0.04212
74.33
1486.6
105
71.5
0.3836
0.0474
66.54
1330.8
90
86.2
0.3708
0.0499
65.5
1310
Force
Joint
Force of
Applied to Compres- Muscle
Cybex sion Force ContracArm (Fc)
(Fy)
tion (F1) Power
(N)
(N)
(N)
(Nm/sec)
300.56667
289.06667
268.83333
247.76667
221.8
218.33333
6116.427
3004.0604
1699.8094
954.53488
445.29486
86.975651
6293.9941
3468.7926
2343.3141
1766.6682
1403.3233
1312.8841
23.606506
22.703296
21.11417
19.459594
17.420172
17.1479
Experiments 2 and 3 – Measured and
Calculated Isokinetic Parameters
(continued)
Maximum Isokinetic (60 deg/sec = 1.0472 rad/sec)
Angle of
Attachm
ent of
Knee
Muscle
Joint
to
Angle
Shank
(Thata 2) (Theta
(deg)
1) (deg)
180
3.41
165
13.64
150
30
135
43.5
120
57.4
105
71.5
90
86.2
Torque
Applie Joint
Force
Muscle Muscle
d to Turning Applied
Length Moment Cybex Force to Cybex
(OI)
Arm
Arm
(Fx)
Arm (Fc)
(m)
(m)
(Nm)
(N)
(N)
0.4207 0.00297
0.4185 0.01179 75.19
1503.8 250.6333
0.4133
0.025
79.8
1596
266
0.4057
0.0344
87.25
1745 290.8333
0.3953 0.04212 74.33
1486.6 247.7667
0.3836
0.0474
70
1400 233.3333
0.3708
0.0499
64.05
1281
213.5
Joint
Compres- Force of
sion
Muscle
Force Contrac(Fy)
tion (F1) Power
(N)
(N)
(Nm/sec)
5100.301
2764.345
1838.913
954.5349
468.4497
85.05024
5248.37
3191.99
2535.08
1766.67
1476.29
1283.82
78.739
83.5666
91.3682
77.8384
73.304
67.0732
Experiments 2 and 3 – Measured and
Calculated Isometric Parameters
(continued)
Maximum Isokinetic (90 deg/sec = 1.5708 rad/sec)
Angle of
Torqu
Attachme
e
Knee
nt of
Applie Joint
Force
Joint
Muscle to Muscle
d to Turning Applied
Angle
Shank
Length Muscle Cybex Force to Cybex
(Theta 2) (Theta 1)
(OI)
Moment Arm
(Fx)
Arm (Fc)
(deg)
(deg)
(m)
Arm (m) (Nm)
(N)
(N)
180
3.41
0.4207 0.00297
165
13.64
0.4185 0.01179 36.59
731.8 121.9667
150
30
0.4133
0.025
65.98
1319.6 219.9333
135
43.5
0.4057
0.0344 72.02
1440.4 240.0667
120
57.4
0.3953 0.04212 76.35
1527
254.5
105
71.5
0.3836
0.0474 69.14
1382.8 230.4667
90
86.2
0.3708
0.0499 58.58
1171.6 195.2667
Joint
Compres- Force of
sion
Muscle
Force Contrac(Fy)
tion (F1) Power
(N)
(N)
(Nm/sec)
2481.979
2285.608
1517.92
980.4754
462.6944
77.78677
2554.034
2639.194
2092.566
1814.679
1458.157
1174.179
57.47557
103.6414
113.129
119.9306
108.6051
92.01746
Experiments 2 and 3 – Measured and
Calculated Isokinetic Parameters
(continued)
Maximum Isokinetic (120 deg/sec = 2.0944 rad/sec)
Angle of
Attachme
Knee
nt of
Joint
Muscle to
Angle
Shank
(Thata 2) (Theta 1)
(deg)
(deg)
180
3.41
165
13.64
150
30
135
43.5
120
57.4
105
71.5
90
86.2
Muscle
Length
(OI)
(m)
0.4207
0.4185
0.4133
0.4057
0.3953
0.3836
0.3708
Torque
Applie Joint
Force
d to Turning Applied
Muscle Cybex Force to Cybex
Moment Arm
(Fx)
Arm (Fc)
Arm (m) (Nm)
(N)
(N)
0.00297
0.01179
53
1060 176.6667
0.025
63.96
1279.2
213.2
0.0344
67.4
1348 224.6667
0.04212 63.09
1261.8
210.3
0.0474
65.1
1302
217
0.0499
30.35
607 101.1667
Joint
Compres- Force of
sion
Muscle
Force Contrac- Power
(Fy)
tion (F1) (Nm/sec
(N)
(N)
)
3595.105
2215.633
1420.547
810.1925
435.6582
40.30093
3699.48
2558.39
1958.33
1499.52
1372.95
608.336
111.003
133.958
141.163
132.136
136.345
63.565
Experiments 2 and 3 – Measured and
Calculated Isokinetic Parameters
(continued)
Maximum Isokinetic (150 deg/sec = 2.6180)
Angle of
Attachm
Knee
ent of
Joint
Muscle
Angle to Shank
(Thata 2) (Theta 1)
(deg)
(deg)
180
3.41
165
13.64
150
30
135
43.5
120
57.4
105
71.5
90
86.2
Muscle
Length
(OI)
(m)
0.4207
0.4185
0.4133
0.4057
0.3953
0.3836
0.3708
Torque
Applie
Joint
d to Turning
Muscle Cybex Force
Moment Arm
(Fx)
Arm (m) (Nm)
(N)
0.00297
0.01179 63.38 1267.6
0.025
66.84 1336.8
0.0344 68.56 1371.2
0.04212 65.68 1313.6
0.0474 63.08 1261.6
0.0499 54.26 1085.2
Joint
Force
Compres- Force of
Applied to
sion
Muscle
Cybex
Force Contrac- Power
Arm (Fc)
(Fy)
tion (F1) (Nm/sec
(N)
(N)
(N)
)
211.26667
222.8
228.53333
218.93333
210.26667
180.86667
4299.203
2315.399
1444.996
843.4529
422.1401
72.05036
4424.01
2673.59
1992.03
1561.08
1330.35
1087.59
165.929
174.987
179.49
171.95
165.143
142.053
Experiments 2 and 3 – Measured and
Calculated Isokinetic Parameters
(continued)
Maximum Isokinetic (180 deg/sec = 3.1416 rad/sec)
Angle of
Attachm
ent of
Knee
Muscle
Joint
to
Angle
Shank
(Thata 2) (Theta
(deg)
1) (deg)
180
3.41
165
13.64
150
30
135
43.5
120
57.4
105
71.5
90
86.2
Torque
Applie Joint
Force
Muscle
d to Turning Applied
Length Muscle Cybex Force to Cybex
(OI)
Moment Arm
(Fx)
Arm (Fc)
(m)
Arm (m) (Nm)
(N)
(N)
0.4207 0.00297
0.4185 0.01179 37.16
743.2 123.8667
0.4133
0.025
54.16
1083.2 180.5333
0.4057
0.0344
60.2
1204 200.6667
0.3953 0.04212 62.52
1250.4
208.4
0.3836
0.0474
60.2
1204 200.6667
0.3708
0.0499
49.36
987.2 164.5333
Joint
Compres- Force of
sion
Muscle
Force Contrac(Fy)
tion (F1) Power
(N)
(N)
(Nm/sec)
2520.644
1876.152
1268.798
802.8726
402.8667
65.54379
2593.82
2166.4
1749.13
1485.97
1269.61
989.373
116.742
170.149
189.124
196.413
189.124
155.069
2b. Neatly plot on one sheet of graph paper
Fx versus 2, Fy versus 2, and F1 versus
2 for maximum isokinetic contractions for
the knee joint angles of 165, 150, 135,
120, 105, and 90 for the three angular
velocities. Use the same scale for this plot
as was used in 2a. For the nine lines,
distinguish between the three parameters
and three angular velocities.
For 2a. and 2b., explain the relationships that
exist between knee joint angle (2) and the force
of muscle contraction (F1), joint turning
component (Fx) of muscular contraction, and
joint compressive component (Fy) of muscular
contraction. Are these relationships similar
between the isometric and isokinetic
contractions? Explain. Is there a pattern, going
from the isometric contractions to faster and
faster isokinetic contractions? In other words, is
there a relationship between
angular velocity and the three force
vectors? Explain.
What interpretation did you make of this
data?
Force vs Knee Angle - Isokinetic
Fx - 15 deg/sec
Fy - 15 deg/sec
8000
F1 - 15 deg/sec
7000
Fx - 90 deg/sec
Fy - 90 deg/sec
Force (N)
6000
F1 - 90 deg/sec
Fx - 180 deg/sec
5000
Fy - 180 deg/sec
F1 - 180 deg/sec
4000
3000
2000
1000
0
180
165
150
135
Knee Angle (deg)
120
105
90
• The same pattern existed in the isokinetic contractions as was
evident in the isometric contractions (see isometric graph).
• A similar pattern is evident among these angular velocities.
Force vs Knee Angle - Isokinetic
Fx - 15 deg/sec
Fy - 15 deg/sec
8000
F1 - 15 deg/sec
7000
Fx - 90 deg/sec
Fy - 90 deg/sec
Force (N)
6000
F1 - 90 deg/sec
Fx - 180 deg/sec
5000
Fy - 180 deg/sec
F1 - 180 deg/sec
4000
3000
2000
1000
0
180
165
150
135
Knee Angle (deg)
120
105
90
• An inverse relationship between force of isokinetic contraction and
angular velocity was expected.
Force vs Knee Angle - Isokinetic
Fx - 15 deg/sec
Fy - 15 deg/sec
8000
F1 - 15 deg/sec
7000
Fx - 90 deg/sec
Fy - 90 deg/sec
Force (N)
6000
F1 - 90 deg/sec
Fx - 180 deg/sec
5000
Fy - 180 deg/sec
F1 - 180 deg/sec
4000
3000
2000
1000
0
180
165
150
135
Knee Angle (deg)
120
105
90
What interpretation did you make of this
data?
Force vs Knee Angle
Fx - 60 deg/sed
Fy - 60 deg/sec
8000
F1 - 60 deg/sec
7000
Fx - 120 deg/sec
Fy - 120 deg/sec
Force (N)
6000
F1 - 120 deg/sec
Fx - 150 deg/sec
5000
Fy - 150 deg/sec
F1 - 150 deg/sec
4000
3000
2000
1000
0
180
165
150
135
Knee Angle (deg)
120
105
90
• The same pattern existed in the isokinetic contractions as was
evident in the isometric contractions (see isometric graph).
• A similar pattern is evident among these angular velocities.
Force vs Knee Angle
Fx - 60 deg/sed
Fy - 60 deg/sec
8000
F1 - 60 deg/sec
7000
Fx - 120 deg/sec
Fy - 120 deg/sec
Force (N)
6000
F1 - 120 deg/sec
Fx - 150 deg/sec
5000
Fy - 150 deg/sec
F1 - 150 deg/sec
4000
3000
2000
1000
0
180
165
150
135
Knee Angle (deg)
120
105
90
• An inverse relationship between force of isokinetic contraction and
angular velocity was expected. This was evident for these angular
velocities.
Force vs Knee Angle
Fx - 60 deg/sed
Fy - 60 deg/sec
8000
F1 - 60 deg/sec
7000
Fx - 120 deg/sec
Fy - 120 deg/sec
Force (N)
6000
F1 - 120 deg/sec
Fx - 150 deg/sec
5000
Fy - 150 deg/sec
F1 - 150 deg/sec
4000
3000
2000
1000
0
180
165
150
135
Knee Angle (deg)
120
105
90
3. Neatly plot on one sheet of graph
paper the force of muscle
contraction (F1) versus muscle
length (OI) for the isometric and
three isokinetic contractions.
Distinguish between the four lines.
Can muscle force-velocity and
length-tension relationships
justify these results? Explain.
What interpretation did you make of this
data?
Maximum Force of Hamstrings vs Muscle Length
8000
7000
F1 - Isometric
F1 - 15 deg/sec
F1 - 60 deg/sec
F1 - 90 deg/sec
6000
F1 - 120 deg/sec
Force (N)
F1 - 150 deg/sec
5000
F1 - 180 deg/sec
4000
3000
2000
1000
0
0.37
0.375
0.38
0.385
0.39
0.395
Muscle Length (m)
0.4
0.405
0.41
0.415
0.42
• A dynamic relationship existed between muscle length and its
ability to exert maximum contractile force for all angular velocities
tested.
Maximum Force of Hamstrings vs Muscle Length
8000
7000
F1 - Isometric
F1 - 15 deg/sec
F1 - 60 deg/sec
F1 - 90 deg/sec
6000
F1 - 120 deg/sec
Force (N)
F1 - 150 deg/sec
5000
F1 - 180 deg/sec
4000
3000
2000
1000
0
0.37
0.375
0.38
0.385
0.39
0.395
Muscle Length (m)
0.4
0.405
0.41
0.415
0.42
• As muscle length increased, there was an increase in its ability to
exert force for all angular velocities. This relationship was relatively
constant between 0.37 and 0.4 meters, but appeared curvilinear and
increased substantially after achieving a muscle length of 0.4 meters.
Maximum Force of Hamstrings vs Muscle Length
8000
7000
F1 - Isometric
F1 - 15 deg/sec
F1 - 60 deg/sec
F1 - 90 deg/sec
6000
F1 - 120 deg/sec
Force (N)
F1 - 150 deg/sec
5000
F1 - 180 deg/sec
4000
3000
2000
1000
0
0.37
0.375
0.38
0.385
0.39
0.395
Muscle Length (m)
0.4
0.405
0.41
0.415
0.42
• The dynamic relationship between muscle length and its ability to
exert maximum force of contraction is likely to be related to the a)
overlap of actin and myosin myofilaments in the sarcomeres and b)
series elastic component of skeletal muscle when length is greater
than “resting” length.
Maximum Force of Hamstrings vs Muscle Length
8000
7000
F1 - Isometric
F1 - 15 deg/sec
F1 - 60 deg/sec
F1 - 90 deg/sec
6000
F1 - 120 deg/sec
Force (N)
F1 - 150 deg/sec
5000
F1 - 180 deg/sec
4000
3000
2000
1000
0
0.37
0.375
0.38
0.385
0.39
0.395
Muscle Length (m)
0.4
0.405
0.41
0.415
0.42
• Even though the isokinetic dynamometer maintained a constant angular velocity
(as opposed to what typically is the case in an isotonic contraction) the following
relationships were evident:
1. Force-velocity: With increased velocity there was a general trend for the knee joint
flexors to be able to exert a decreased maximum force of contraction. This is also
typical of what is seen in maximum isotonic contractions.
Maximum Force of Hamstrings vs Muscle Length
8000
7000
F1 - Isometric
F1 - 15 deg/sec
F1 - 60 deg/sec
F1 - 90 deg/sec
6000
F1 - 120 deg/sec
Force (N)
F1 - 150 deg/sec
5000
F1 - 180 deg/sec
4000
3000
2000
1000
0
0.37
0.375
0.38
0.385
0.39
0.395
Muscle Length (m)
0.4
0.405
0.41
0.415
0.42
• Even though the isokinetic dynamometer maintained a constant angular velocity
(as opposed to what typically is the case in an isotonic contraction) the following
relationships were evident:
2. Length-tension: A curvilinear relationship between maximum force of contraction
and muscle length was evident. This is somewhat similar to what is typical at the
muscle fiber level in which maximum force of contraction is dependent on the
interaction between the overlap of the actin and myosin myofilaments and the tension
associated with theseries and parallel elastic components
Maximum Force of Hamstrings vs Muscle Length
8000
7000
F1 - Isometric
F1 - 15 deg/sec
F1 - 60 deg/sec
F1 - 90 deg/sec
6000
F1 - 120 deg/sec
Force (N)
F1 - 150 deg/sec
5000
F1 - 180 deg/sec
4000
3000
2000
1000
0
0.37
0.375
0.38
0.385
0.39
0.395
Muscle Length (m)
0.4
0.405
0.41
0.415
0.42
4. Neatly plot on one sheet of graph paper
the mechanical advantage (moment arm) of
the hamstrings to the knee joint center
versus F1 for the isometric and isokinetic
contractions for the knee joint angles of
165, 150, 135, 120, 105, and 90.
Distinguish between the four lines.
Is there an inverse relationship
between mechanical advantage and F1?
Explain.
What interpretation did you make of this
data?
Maximum Force of Hamstring Contraction vs Muscle Moment Arm
F1 - Isometric
8000
F1 - 15 deg/sec
7000
F1 - 60 deg/sec
F1 - 90 deg/sec
Force (N)
6000
F1 - 120 deg/sec
F1 - 150 deg/sec
5000
F1 - 180 deg/sec
4000
3000
2000
1000
0
0.01
0.015
0.02
0.025
0.03
0.035
Muscle Moment Arm (m)
0.04
0.045
0.05
0.055
• For all angular velocities (including the isometric condition), there
was an inverse relationship between muscle moment arm and the
muscle’s ability to exert maximum force of contraction.
Maximum Force of Hamstring Contraction vs Muscle Moment Arm
F1 - Isometric
8000
F1 - 15 deg/sec
7000
F1 - 60 deg/sec
F1 - 90 deg/sec
Force (N)
6000
F1 - 120 deg/sec
F1 - 150 deg/sec
5000
F1 - 180 deg/sec
4000
3000
2000
1000
0
0.01
0.015
0.02
0.025
0.03
0.035
Muscle Moment Arm (m)
0.04
0.045
0.05
0.055
5. Neatly plot on one sheet of graph
paper the mechanical advantage
(moment arm) of the hamstrings to the
knee joint center versus and the muscle
length (OI) of the hamstring muscles.
What is the relationship
between mechanical advantage and
hamstring length? Explain.
What interpretation did you make of this
data?
Hamstring Moment Arm vs Muscle Length
0.43
Muscle Length (m)
0.42
0.41
0.4
0.39
0.38
0.37
0
0.01
0.02
0.03
Muscle Moment Arm (m)
0.04
0.05
0.06
• A curvilinear relationship existed between muscle length and
muscle moment arm.
• As the muscle moment arm increased, the muscle length decreased.
Hamstring Moment Arm vs Muscle Length
0.43
Muscle Length (m)
0.42
0.41
0.4
0.39
0.38
0.37
0
0.01
0.02
0.03
Muscle Moment Arm (m)
0.04
0.05
0.06
• There appears to a compensatory mechanism in place. The
mechanical advantage associated with a longer muscle moment arms
is detracted by the loss in ability of the muscle to exert force due to
decreases in its length. The opposite is also evident.
Hamstring Moment Arm vs Muscle Length
0.43
Muscle Length (m)
0.42
0.41
0.4
0.39
0.38
0.37
0
0.01
0.02
0.03
Muscle Moment Arm (m)
0.04
0.05
0.06
6. Neatly plot on one sheet of graph paper
[(Fx)(AI)] versus 2 and [(Fc)(AC)] versus 2 for the
isokinetic contractions of 30/second [(/6)
(radians/second)] for the knee joint angles of 165,
150, 135, 120, 105, and 90. Note that clockwise
moments about the knee joint center (A) are negative
and counterclockwise moments are positive.
Distinguish between the two lines. An isokinetic
dynamometer is said to provide “accommodating
resistance.” Explain this relationship in regard to
constant angular velocity.
What interpretation did you make of this
data?
Isokinetic Torque vs Knee Angle
100
80
(Fx)(AI) -15 deg/sec
60
(Fc)(AC) -15 deg/sec
(Fx)(AI) - 60 deg/sec
Torque (Nm)
40
20
0
-20
-40
(Fc)(AC) - 60 deg/sec
(Fx)(AI) - 90 deg/sec
(Fc)(AC) = 90 deg/sec
(Fx)(AI) - 120 deg/sec
(Fc)(AC) - 120 deg/sec
(Fx)(AI) - 150 deg/sec
(Fc)(AC) - 150 deg/sec
(Fx)(AI) - 180 deg/sec
-60
(Fc)(AC) - 180 deg/sec
-80
-100
180
165
150
135
Knee Angle (deg)
120
105
90
• For all angular velocities, the torque experienced by the arm of the
isokinetic dynamometer was equal and opposite to the torque
experienced by the subject’s shank. This is to be expected since the
angular velocity of the isokinetic dynamometer is constant for all
settings.
Isokinetic Torque vs Knee Angle
100
80
(Fx)(AI) -15 deg/sec
60
(Fc)(AC) -15 deg/sec
(Fx)(AI) - 60 deg/sec
Torque (Nm)
40
20
0
-20
-40
(Fc)(AC) - 60 deg/sec
(Fx)(AI) - 90 deg/sec
(Fc)(AC) = 90 deg/sec
(Fx)(AI) - 120 deg/sec
(Fc)(AC) - 120 deg/sec
(Fx)(AI) - 150 deg/sec
(Fc)(AC) - 150 deg/sec
(Fx)(AI) - 180 deg/sec
-60
(Fc)(AC) - 180 deg/sec
-80
-100
180
165
150
135
Knee Angle (deg)
120
105
90
7.
Neatly plot on one sheet of graph paper power
versus angular velocity for the three isokinetic
contraction conditions for the knee joint angles of
165, 150, 135, 120, 105, and 90.
What relationship exists between power and
angular velocity? Explain. What relationship
exists between maximum power in each of the
three isokinetic contraction conditions and the
joint angle at which it occurred? What are
plausible explanations for this relationship?
What interpretation did you make of this
data?
Power vs Angular Velocity for Selected Knee Angles
210
180
Power (Nm/sec)
15 deg/sec
150
60 deg/sec
90 deg/sec
120
120 deg/sec
150 deg/sec
90
180 deg/sec
60
30
0
180
165
150
135
Knee Angle (deg)
120
105
90
• Power is the product of torque and angular velocity.
• It was previously interpreted that there was a general inverse
relationship between angular velocity and the ability of muscle to
generate maximum torque.
Power vs Angular Velocity for Selected Knee Angles
210
180
Power (Nm/sec)
15 deg/sec
150
60 deg/sec
90 deg/sec
120
120 deg/sec
150 deg/sec
90
180 deg/sec
60
30
0
180
165
150
135
Knee Angle (deg)
120
105
90
• A direct relationship between the muscle’s ability to generate
power and angular velocity is evident.
• Of the two factors in determining power (torque and angular
velocity), angular velocity appears to dominate.
Power vs Angular Velocity for Selected Knee Angles
210
180
Power (Nm/sec)
15 deg/sec
150
60 deg/sec
90 deg/sec
120
120 deg/sec
150 deg/sec
90
180 deg/sec
60
30
0
180
165
150
135
Knee Angle (deg)
120
105
90
8.
What effects could internal anatomical
differences in the locations of muscle
origins and insertions and bone (lever)
lengths have on internally measured
forces and torques? In other words,
what effects would changes in AI, AB,
and OB have on internally measured
forces and torques? How would these
effects manifest themselves in external
measures of forces and torques?
(See next slide for model figure.)
Influence
of
Changes
in AI,
AB, and
OB?
Other
Changes?
Definition of Variables
F1 – maximum force of hamstring contraction
Fc – maximum force applied at pad on mechanical arm
Fx –vector component of F1 perpendicular to rigid shaft of
shank; turning component of F1 at collective insertion (I)
of hamstrings
Fy – vector component of F1 parallel to rigid shaft of shank;
joint compressive component of F1 at collective
insertion (I) of hamstrings
1 – angle between shaft of shank and F1 at I
2 – angle at knee joint center (A) formed by shafts
of the thigh and shank
AI – distance between collective insertion of hamstrings (I)
and knee joint center (A); AI = _______ meters
AC – distance from center of cuff to knee joint center (A);
AC = _______ meters
AB – horizontal distance from knee joint center (A) to
a point B located directly above the collective origin
(O) of the hamstrings; AB = _______ meters
OI – hamstring muscle length
OB – distance from O to B; OB = _______ meters
OP – distance from O to point P on shaft of shank, OP is
parallel to AB
AS – perpendicular line from A to O
AM – a line from point A that intersects OI, forming a right
angle; moment arm of F1 (not drawn on figure)
9. Several assumptions have been
provided about this Hypothetical Model.
List at least five additional assumptions
which cause this model to be
hypothetical as opposed to an actual
model. For each of these assumptions,
conjecture as to its potential influence
on the results of the experiment (i.e.,
major or minor) and why you think this
way.
Additional Assumptions
1. Two-dimensional versus threedimensional model
2. Use of cadaver data
3. Other?
Force Platform Lecture