Download A similar pattern is evident among these angular velocities. An

Lecture XIII Assignment
1.
Abstract a research article that utilizes a force platform to
collect data. The article should be related to your academic
area of interest. Be prepared to give a 10 minute presentation
in the next class. Concentrate your presentation and abstract
on the methods, procedures, and technical aspects of the use of
the force platform.
2.
Solve problems 1 and 2 in 5.6 Problems Based on Kinetic and
Kinematic Data in our class text.
3.
Work on completing the force platform laboratory experiment.
It is due at the time of the final examination.
Lecture Topics
1. Examination on models and calculation of
joint reaction forces and net muscle
moments
2. Review of results from internal model lab
3. Force platform lecture
4. Force platform experiment
1. Examination
(60 minute limit)
2. Review of Results from Internal
Model Lab
 Internal Model Experiment
 Internal Model Subject
Information and Data Sheet
Motivated
subject?
Limitations Associated with
Experiments
• Single subject design
• Precision in the positioning of the subject
• Motivation level of the subject throughout the
experiment
• Internal model representing reality
• Others
--------------------------------------------------------

LIMITED GENERALIZABILITY OF RESULTS
Mr. Accuracy?
Experiment 1
Comparison of Cadaver-Based
Measurements of the Moments of Foot
and Shank Segments (Multi-Segment
System) and Experimentally Measured
Moments
Similar
to
Cadaver
Data?
Experiment 1 – Measured and Calculated
Parameters
Free Fall at 26 degrees/second
Shank and Foot
Bar Only
Shank
Shank Calculated Angle
Angle
Torque Below
Below (Nm) from HoriIntended/
Horizontal Anthro- zontal Actual Angle Torque
(deg)
pometry (deg) (Rad) Used (Nm)
0
7.995
0
3.14/3.145
15
7.72
15
2.88/2.876 4.899
30
6.92
30
2.618/2.607 4.625
45
5.65
45
2.356/2.371 4.625
60
4
60
2.094/2.102 3.259
75
2.069
75
xxx
90
0
90
xxx
1.62
Shank, Foot, and Bar
Intended
Shank
Angle
Shank
Below Intended/
Hori- Actual Angle Torque
zontal (Rad) Used (Nm)
0
15
2.88/2.88 15.55
30
2.618/2.614 13.37
2.356/2.345
45
2
8.997
2.094/2.109
60
2
5.992
1.833/1.874
75
2
1.703
90
1.571
Static Condition (0 Angular
Velocity) and No Muscular
Contraction
Shank, Foot, and Bar
Intended
Shank
Shank
Angle Intended/
Below
Actual
Hori- Angle (Rad) Torque
zontal
Used
(Nm)
0
15
2.88/2.85 15.28
30
2.618/2.614 17.47
2.356/2.345
45
2
14.19
2.094/2.109
60
2
10.09
1.833/1.807
75
2
5.445
1.571/1.605
90
2
4.625
Torque (Nm)
Free Fall
at 26
degrees/ Anthrosecond pometry Sum
Shank
Angle
Below
Horizontal
(deg)
0
15
30
4.899
4.625
45
4.625
5.65
10.275
60
3.259
4
7.259
75
1.62
2.069
3.689
90
Bar
Shank,
Foot,
Shank
and
and Foot Bar
7.995
7.72 12.619
6.92 11.545
0
Torque (Nm)
What interpretation did you make of this data?
20
Shank and Foot - Anthropometry
18
Bar Only - Free Fall (26 deg/sec)
16
Shank, Foot, and Bar - Free Fall (26 deg/sec)
14
Shank, Foot, and Bar - Static (0 deg/sec)
Sum of Anthropometry and Bar Only
12
10
8
6
4
2
0
0
15
30
45
60
75
Shank or Corresponding Angle of Shank Below Horizontal (deg)
90
Torque (Nm)
• Calculated torque from anthropometry plus bar approximates
measured static and free fall torque of shank, foot, and bar.
20
Shank and Foot - Anthropometry
18
Bar Only - Free Fall (26 deg/sec)
16
Shank, Foot, and Bar - Free Fall (26 deg/sec)
14
Shank, Foot, and Bar - Static (0 deg/sec)
Sum of Anthropometry and Bar Only
12
10
8
6
4
2
0
0
15
30
45
60
75
Shank or Corresponding Angle of Shank Below Horizontal (deg)
90
Experiments 2 and 3
 Raw Data Files
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
Budding Researchers?
Experiments 2 and 3 – Measured and
Calculated Isometric Parameters
Angle of
Attachment
Knee Joint of Muscle
Angle
to Shank
(Theta 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
Maximum Isometric (0 deg/sec)
Torque
Joint
Applied Joint
Force Compres- Force of
to
Turning Applied to
sion
Muscle
Muscle Cybex Force
Cybex
Force ContracMoment
Arm
(Fx)
Arm (Fc)
(Fy)
tion (F1) Power
Arm (m) (Nm)
(N)
(N)
(N)
(N)
(Nm/sec)
0.00297
0.01179 81.953 1639.06 273.1767 6754.4 6950.45
0
0.025
71.023 1420.46 236.7433 2460.31 2840.92
0
0.0344 75.395 1507.9 251.3167 1152.62 2190.59
0
0.04212 80.314 1606.28 267.7133 1027.26 1906.67
0
0.0474 77.581 1551.62 258.6033 519.16 1636.17
0
0.0499 63.919 1278.38 213.0633
84.96
1281.97
0
What interpretation did you make of this data?
Maximum Force vs Knee Angle - Isometric
7000
6000
Fx
Fy
F1
Force (N)
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.
Maximum Force vs Knee Angle - Isometric
7000
6000
Fx
Fy
F1
Force (N)
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.
Maximum Force vs Knee Angle - Isometric
7000
6000
Fx
Fy
F1
Force (N)
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
nt of
Knee Joint Muscle to
Angle
Shank
(Theta 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
Applied
Joint
Force
to
Turning Applied to
Muscle Cybex Force Cybex Arm
Moment Arm
(Fx)
(Fc)
Arm (m) (Nm)
(N)
(N)
0.00297
0.01179 52.989 1059.78
176.63
0.025 89.057 1781.14 296.85667
0.0344 95.615 1912.3 318.71667
0.04212 72.663 1453.26
242.21
0.0474 59.001 1180.02
196.67
0.0499 27.304 546.08 91.013333
Joint
Compression
Force
(Fy)
(N)
4367.25
3085.02
2015.16
929.38
384.82
36.27
Force of
Muscle
Contraction (F1) Power
(N)
(Nm/sec)
4494
3562.28
2778.1
1725
1244.3
547.28
13.87
23.32
25.03
19.02
15.45
7.15
Experiments 2 and 3 – Measured and
Calculated Isokinetic Parameters
(continued)
Maximum Isokinetic (60 deg/sec = 1.0472 rad/sec)
Angle of
Attachm
Knee
ent of
Joint
Muscle Muscle
Angle to Shank Length
(Theta 2) (Theta 1)
(OI)
(deg)
(deg)
(m)
180
3.41
0.4207
165
13.64
0.4185
150
30
0.4133
135
43.5
0.4057
120
57.4
0.3953
105
71.5
0.3836
90
86.2
0.3708
Torque
Joint
Applied Joint
Force Compres- Force of
to
Turning Applied
sion
Muscle
Muscle Cybex Force to Cybex
Force ContracMoment
Arm
(Fx)
Arm (Fc)
(Fy)
tion (F1) Power
Arm (m) (Nm)
(N)
(N)
(N)
(N)
(Nm/sec)
0.00297
0.01179 69.657 1393.14 232.19 5740.99 5907.6
72.94
0.025
81.953 1639.06 273.177 2838.94 3278.12 85.82
0.0344
91.79 1835.8 305.967 1934.53 2666.94 96.12
0.04212 88.784 1775.68 295.947 1135.59 2107.75 92.97
0.0474 81.406 1628.12 271.353 544.76 1716.84 85.25
0.0499 71.843 1436.86 239.477
95.44
1440.03 75.23
Experiments 2 and 3 – Measured and
Calculated Isometric Parameters
(continued)
Maximum Isokinetic (90 deg/sec = 1.5708 rad/sec)
Angle of
Attachment
Knee Joint of Muscle
to Shank
Angle
(Theta 2) (Theta 1)
(deg)
(deg)
3.41
180
13.64
165
30
150
43.5
135
57.4
120
71.5
105
86.2
90
Muscle
Length
(OI)
(m)
0.4207
0.4185
0.4133
0.4057
0.3953
0.3836
0.3708
Torque
Applied Joint
Turning
to
Muscle Cybex Force
(Fx)
Moment Arm
(N)
Arm (m) (Nm)
0.00297
0.01179 75.668 1513.36
0.025 78.674 1573.48
0.0344 82.226 1644.52
0.04212 80.04 1600.8
0.0474 80.04 1600.8
0.0499 66.925 1338.5
Joint
Compres- Force of
Force
Muscle
sion
Applied to
ContracForce
Cybex
Power
tion (F1)
(Fy)
Arm (Fc)
(Nm/sec)
(N)
(N)
(N)
252.2267
262.2467
274.0867
266.8
266.8
223.0833
6236.41
2725.35
1732.99
1023.77
535.61
88.9
6417.4
3146.96
2389.1
1900.2
1688
1341.4
118.86
123.58
129.16
125.73
125.73
105.13
Experiments 2 and 3 – Measured and
Calculated Isokinetic Parameters
(continued)
Maximum Isokinetic (120 deg/sec = 2.0944 rad/sec)
Angle of
Torque
Joint
Attachment
Applied Joint
Force Compres- Force of
Knee Joint of Muscle Muscle
to
Turning Applied to
sion
Muscle
Angle
to Shank Length Muscle Cybex Force
Cybex
Force Contrac(Theta 2) (Theta 1)
(OI)
Moment
Arm
(Fx)
Arm (Fc)
(Fy)
tion (F1) Power
(deg)
(deg)
(m)
Arm (m) (Nm)
(N)
(N)
(N)
(N)
(Nm/sec)
180
0.4207 0.00297
165
0.4185 0.01179 64.739 1294.78 215.7967 5335.65 5490.5 135.59
150
0.4133
0.025
74.849 1496.98 249.4967 2592.85 2993.96 156.76
135
0.4057 0.0344 79.221 1584.42 264.07
1669.63 2301.75 165.92
120
0.3953 0.04212 77.035 1540.7 256.7833 985.31 1828.82 161.34
105
0.3836 0.0474 72.663 1453.26 242.21
465.25 1532.45 152.19
90
0.3708 0.0499 63.099 1261.98 210.33
83.82
1264.76 132.15
Experiments 2 and 3 – Measured and
Calculated Isokinetic Parameters
(continued)
Maximum Isokinetic (150 deg/sec = 2.6180)
Angle of
Attachme
nt of
Knee Joint Muscle to
Angle
Shank
(Theta 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
Joint
Applied
Joint
Force
Compres- Force of
to
Turning Applied to
sion
Muscle
Muscle Cybex Force Cybex Arm Force ContracMoment Arm
(Fx)
(Fc)
(Fy)
tion (F1) Power
Arm (m) (Nm)
(N)
(N)
(N)
(N)
(Nm/sec)
0.00297
0.01179
0.025 69.384 1387.68
231.28
2403.53 2775.36 181.65
0.0344 64.465 1289.3 214.88333 1358.64 1873.02 168.77
0.04212 55.722 1114.44
185.74
712.71 1322.85 145.88
0.0474 53.536 1070.72 178.45333 358.26 1129.07 140.16
0.0499 38.781 775.62
129.27
51.52
777.33 101.53
Experiments 2 and 3 – Measured and
Calculated Isokinetic Parameters
(continued)
Maximum Isokinetic (180 deg/sec = 3.1416 rad/sec)
Angle of
Attachm
Knee
ent of
Joint
Muscle Muscle
Angle to Shank Length
(Theta 2) (Theta 1)
(OI)
(deg)
(deg)
(m)
180
3.41
0.4207
165
13.64
0.4185
150
30
0.4133
135
43.5
0.4057
120
57.4
0.3953
105
71.5
0.3836
90
86.2
0.3708
Torque
Joint
Applied Joint
Force Compres- Force of
to
Turning Applied
sion
Muscle
Muscle Cybex Force to Cybex
Force ContracMoment
Arm
(Fx)
Arm (Fc)
(Fy)
tion (F1) Power
Arm (m) (Nm)
(N)
(N)
(N)
(N)
(Nm/sec)
0.00297
0.01179 55.995 1119.9 186.65 4614.96 4748.9 175.91
0.025
64.739 1294.78 215.797 2242.62 2589.56 203.38
0.0344 64.465 1289.3 214.883 1358.63
1873
202.52
0.04212 61.46 1229.2 204.867 786.12
1459.1 193.08
0.0474 56.541 1130.82 188.47
378.35
1192.4 177.63
0.0499 48.891 977.82 162.97
64.95
980
153.6
What interpretation did you make of this data?
Maximum Force vs Knee Angle - Isokinetic
7000
Fx - 15 deg/sec
Fy - 15 deg/sec
F1 - 15 deg/sec
Fx - 90 deg/sec
Fy - 90 deg/sec
F1 - 90 deg/sec
Fx - 180 deg/sec
Fy - 180 deg/sec
F1 - 180 deg/sec
6000
Force (N)
5000
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 these isometric contractions (see isometric graph).
• A similar pattern is evident among these angular velocities.
Maximum Force vs Knee Angle - Isokinetic
7000
Fx - 15 deg/sec
Fy - 15 deg/sec
F1 - 15 deg/sec
Fx - 90 deg/sec
Fy - 90 deg/sec
F1 - 90 deg/sec
Fx - 180 deg/sec
Fy - 180 deg/sec
F1 - 180 deg/sec
6000
Force (N)
5000
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 not evident at the 165
degree knee angle for these angular velocities, but was evident in the
middle knee angles.
Maximum Force vs Knee Angle - Isokinetic
7000
Fx - 15 deg/sec
Fy - 15 deg/sec
F1 - 15 deg/sec
Fx - 90 deg/sec
Fy - 90 deg/sec
F1 - 90 deg/sec
Fx - 180 deg/sec
Fy - 180 deg/sec
F1 - 180 deg/sec
6000
Force (N)
5000
4000
3000
2000
1000
0
180
165
150
135
Knee Angle (deg)
120
105
90
What interpretation did you make of this data?
Maximum Force vs Knee Angle
7000
Fx - 60 deg/sed
Fy - 60 deg/sec
F1 - 60 deg/sec
Fx - 120 deg/sec
Fy - 120 deg/sec
F1 - 120 deg/sec
Fx - 150 deg/sec
Fy - 150 deg/sec
F1 - 150 deg/sec
6000
Force (N)
5000
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 these isometric contractions (see isometric graph).
• A similar pattern is evident among these angular velocities.
Maximum Force vs Knee Angle
7000
Fx - 60 deg/sed
Fy - 60 deg/sec
F1 - 60 deg/sec
Fx - 120 deg/sec
Fy - 120 deg/sec
F1 - 120 deg/sec
Fx - 150 deg/sec
Fy - 150 deg/sec
F1 - 150 deg/sec
6000
Force (N)
5000
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.
Maximum Force vs Knee Angle
7000
Fx - 60 deg/sed
Fy - 60 deg/sec
F1 - 60 deg/sec
Fx - 120 deg/sec
Fy - 120 deg/sec
F1 - 120 deg/sec
Fx - 150 deg/sec
Fy - 150 deg/sec
F1 - 150 deg/sec
6000
Force (N)
5000
4000
3000
2000
1000
0
180
165
150
135
Knee Angle (deg)
120
105
90
What interpretation did you make of this data?
Maximum Force of Hamstrings vs Muscle Length
7000
6000
Force (N)
5000
F1 F1 F1 F1 F1 F1 F1 -
Isometric
15 deg/sec
60 deg/sec
90 deg/sec
120 deg/sec
150 deg/sec
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
7000
6000
Force (N)
5000
F1 F1 F1 F1 F1 F1 F1 -
Isometric
15 deg/sec
60 deg/sec
90 deg/sec
120 deg/sec
150 deg/sec
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
7000
6000
Force (N)
5000
F1 F1 F1 F1 F1 F1 F1 -
Isometric
15 deg/sec
60 deg/sec
90 deg/sec
120 deg/sec
150 deg/sec
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
7000
6000
Force (N)
5000
F1 F1 F1 F1 F1 F1 F1 -
Isometric
15 deg/sec
60 deg/sec
90 deg/sec
120 deg/sec
150 deg/sec
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
What interpretation did you make of this data?
Maximum Force of Hamstring Contraction vs Muscle Moment Arm
7000
F1 F1 F1 F1 F1 F1 F1 -
6000
Force (N)
5000
Isometric
15 deg/sec
60 deg/sec
90 deg/sec
120 deg/sec
150 deg/sec
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
7000
F1 F1 F1 F1 F1 F1 F1 -
6000
Force (N)
5000
Isometric
15 deg/sec
60 deg/sec
90 deg/sec
120 deg/sec
150 deg/sec
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
• The mechanical advantage of an increased muscle moment arm
was not able to compensate for a corresponding decrease in
maximum force of muscle contraction.
Maximum Force of Hamstring Contraction vs Muscle Moment Arm
7000
F1 F1 F1 F1 F1 F1 F1 -
6000
Force (N)
5000
Isometric
15 deg/sec
60 deg/sec
90 deg/sec
120 deg/sec
150 deg/sec
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
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
What interpretation did you make of this data?
Maximum Isokinetic Torque vs Knee Angle
100
80
60
(Fx)(AI) -15 deg/sec
(Fc)(AC) -15 deg/sec
Torque (Nm)
40
(Fx)(AI) - 60 deg/sec
(Fc)(AC) - 60 deg/sec
20
(Fx)(AI) - 90 deg/sec
(Fc)(AC) = 90 deg/sec
0
(Fx)(AI) - 120 deg/sec
(Fc)(AC) - 120 deg/sec
-20
(Fx)(AI) - 150 deg/sec
(Fc)(AC) - 150 deg/sec
-40
(Fx)(AI) - 180 deg/sec
(Fc)(AC) - 180 deg/sec
-60
-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 leg. This is to be expected since the
angular velocity of the isokinetic dynamometer is constant for all
settings.
Maximum Isokinetic Torque vs Knee Angle
100
80
60
(Fx)(AI) -15 deg/sec
(Fc)(AC) -15 deg/sec
Torque (Nm)
40
(Fx)(AI) - 60 deg/sec
(Fc)(AC) - 60 deg/sec
20
(Fx)(AI) - 90 deg/sec
(Fc)(AC) = 90 deg/sec
0
(Fx)(AI) - 120 deg/sec
(Fc)(AC) - 120 deg/sec
-20
(Fx)(AI) - 150 deg/sec
(Fc)(AC) - 150 deg/sec
-40
(Fx)(AI) - 180 deg/sec
(Fc)(AC) - 180 deg/sec
-60
-80
-100
180
165
150
135
Knee Angle (deg)
120
105
90
What interpretation did you make of this data?
Power vs Angular Velocity for Selected Knee Angles
210
180
Power (Nm/sec)
150
120
90
15 deg/sec
60 deg/sec
90 deg/sec
120 deg/sec
150 deg/sec
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)
150
120
90
15 deg/sec
60 deg/sec
90 deg/sec
120 deg/sec
150 deg/sec
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)
150
120
90
15 deg/sec
60 deg/sec
90 deg/sec
120 deg/sec
150 deg/sec
180 deg/sec
60
30
0
180
165
150
135
Knee Angle (deg)
120
105
90
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)
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?
Thanks Miguel!!!
3. Force Platform Lecture
4. Force Platform Lab
 Laboratory Experiments: Measurement and
Interpretation of Ground Reaction Forces, Center
of Pressure, and Impulse-Momentum
Relationships