ADVANCED BIOMECHANICS OF PHYSICAL ACTIVITY
Laboratory Experiments: Measurement and Interpretation of Muscle Force
Vectors, Moments, and Power for Knee Flexion
Dr. Eugene W. Brown
Department of Kinesiology
Michigan State University
Purpose:
This laboratory experiment has several purposes:
1.
introduce students to the concepts of biomechanical models in solving
problems,
2.
introduce procedures for the calibration of research instrumentation,
3.
demonstrate relationships between external and internal measures of force and
torque,
4.
review relationships between muscle length and its ability to exert force,
5.
demonstrate changes in the mechanical advantage of muscle with changes in
the angle of the joint it crosses,
6.
demonstrate the relationships between muscular power and joint angular
velocity,
7.
demonstrate the resolution of the force of muscle contraction into a joint
compressive and joint turning component,
8.
show the dynamic interaction between the mechanical advantage of muscle
contraction-joint angle and the force-length relationship of muscle,
9.
explain how to make appropriate assumptions in constructing biomechanical
models, and
10. reveal how small changes in measurements associated with internal models
may influence large changes on the interpretation of biomechanical
parameters.
List of Equipment and Supplies:
1.
APAS system and software for recording and displaying the histories of
torque and joint angle
2.
isokinetic dynamometer with attachments for knee flexion torque and
the ability to set various constant angular velocities
3.
subject without orthopedic problems in the knee joint
4.
anthropometric tools: tape measure, bow caliper, and anthropometer
5.
anatomical charts showing the bony structures and the origins and insertions
of muscles of the lower extremity
6.
9V batteries
7.
weight scale
8.
known weights for loading the isokinetic dynamometer
9.
level
10. mechanical goniometer
11. athletic tape
12.
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)
1.
2.
Some Assumptions
a.
The knee joint is a hinge joint.
b.
The knee joint is frictionless and pinned.
c.
A two dimensional model does not substantially alter the biomechanical
parameters calculated for this three dimensional system.
d.
The subject actually provides maximum knee flexion force for the
isometric and isokinetic contractions at specified angles and throughout
the range of movement.
e.
The weight of the mechanical arm of the isokinetic dynamometer does
not substantially alter the results.
f.
Neglecting the moment of the mechanical arm of the isokinetic
dynamometer does not substantially alter the biomechanical parameters
calculated for this three dimensional system.
Measurements - Using the figure of the Hypothetical Model of the lower
extremity, accurately make the following measurements:
a.
distance from the knee joint center (A) to the center of the isokinetic
dynamometer cuff (C); (AC) = __________ meters
b.
horizontal distance from the knee joint center (A) to a point (B) located
directly above the collective origin (O) of the hamstring muscles (ischeal
tuberosity); AB = _________ meters
c.
perpendicular distance from the origin (O) of the hamstring muscles
(ischeal tuberosity) to the horizontal line representing the femur when
the subject(s) assumes a standard seated position; OB = _______ meters
d.
estimated distance from the collective insertion (I) of the hamstring
muscles to the center of the knee joint (A); AI = __________ meters
General Methods and Procedures:
There will be three experiments conducted to highlight the different purposes of this
laboratory. The students must share the responsibility of carrying out these
experiments. The general methods and procedures for each of these experiments are as
follows:
1.
Anthropometric Measurements
a.
Accurately measure the height (in meters) of the subject with a long
anthropometer and the weight of the subject (in Newtons) with a weight
scale. For these measurements, the subject should be dressed in minimal
clothing and with no shoes.
b.
Using Table 3.1 (Anthropometric Data) in Biomechanics and Motor
Control of Human Movement by David A. Winter and the measured
total body weight and height, determine the weight (in Newtons) of the
shank and foot segments (multi-segment system) and the Cartesian
coordinates (in meters) of the center of mass of this multi-segment
system from the center of the knee joint when the line representing the
shank is horizontal and the ankle is in maximum plantar flexion. Note
that the foot should be fixed (possibly taped) in this position and this
position should be maintained for all subsequent measures of knee
flexion torque. By plantar flexing the ankle, the gastrocnemius is in a
2.
3.
4.
shortened state and its contribution, as a two joint muscle, to knee joint
flexion torque is minimized.
Calibration (see Calibration Procedures on the last page)
a.
Calibrate the torque readings of the isokinetic dynamometer by using
known weights and moment arms as input to the APAS system. If
possible, use weights that create torques in the range of expected
minimum to maximum torque values of knee flexion for the subject.
b.
Calibrate the goniometer output of the isokinetic dynamometer by using
a mechanical goniometer and/or level to establish a horizontal to vertical
range (90) for the mechanical arm of the dynamometer. Determine the
offset between the mechanical arm of the isokinetic dynamometer and
the line representing the shank of the subject.
Subject Preparation
a.
Before collecting data in each of the experiments, the subject should be
familiarized with the setting and tasks to be performed.
b.
It is appropriate to provide a warm up and a few practice trials. This
may reduce the use of antagonistic muscle contraction, typical of the
early learning phase of a motor skill; increase the reproducibility of the
performance; and reduce the chance of injury.
Data Collection
a.
Records saved and subsequently printed from each experiment must be
properly identified with the following information: name of subject, type
of physical activity performed, and angular velocity setting of the
isokinetic dynamometer.
Specific Methods and Procedures:
In addition to the general methods and procedures, the three individual experiments have
their own specific methods and procedures that must be followed.
Experiment 1 – Comparison of Cadaver-Based Measurements of the Moments of
Foot and Shank Segments (Multi-Segment System) and Experimentally Measured
Moments
a.
Set the isokinetic dynamometer at 15/second [(/12)(radians/second)]
and record the torque of the mechanical arm in free fall from a
horizontal position (180) to a vertical position (90). Use a low
sampling rate (100Hz).
b.
Affix the subject to the knee flexion attachment of the isokinetic
dynamometer and use a mechanical goniometer to determine the offset
angle between the shank of the subject and arm of the attachment.
c.
Determine the values of the torques of the shank and foot segments
(multi-segment system), relative to knee angles, by having the subject
assume a relaxed position (no muscular contraction in the lower
extremity) with this multi-segment system at knee angles from 180
(straight knee) to 90 (posterior knee angle) in increments of 15. For
each measurement, the angular velocity of the isokinetic dynamometer
should be set at 0/second (0 radians/second) and the foot should be in a
maximum plantar flexed position. Use a low sampling rate (100Hz).
d.
Determine the values of the torques of the shank and foot segments
(multi-segment system), relative to knee angles, by having the subject
assume a relaxed position (no muscular contraction in the lower
extremity) with this multi-segment system at knee angles from 180
(straight knee) to 90 (posterior knee angle). For this process, set the
angular velocity of the isokinetic dynamometer to 15/second
[(/12)(radians/second)] and record the torque-time and knee angletime histories beginning with the knee fully extended. The foot should
be in a maximum plantar flexed position throughout the movement. Use
a low sampling rate (100Hz).
e.
Determine the values of the torques of the shank and foot segments
(multi-segment system), relative to knee angles, by using anthropometric
data from the subject’s height and weight and proportion data from
cadavers provided in Table 3.1 (Winter, 1990, second edition). Assume
a maximum plantar flexed foot position.
Experiment 2 – Biomechanics of Maximum Isometric Knee Flexion Torque for
Various Knee Joint Angles
a.
Record the maximum isometric torques for knee angles of 165, 150,
135, 120, 105, and 90. Use a low sampling rate (100Hz).
b.
Randomize the order of the knee joint angle used and provide sufficient
rest between trials to minimize the influence of fatigue.
Experiment 3 – Biomechanics of Maximum Isokinetic Knee Flexion Torque for
Various Knee Joint Angles and Angular Velocities
a.
Record the torque-time and knee angle-time histories for maximum
isokinetic knee flexion at angles from 180 to 90 for isokinetic
dynamometer angular velocities of 30/second [(/6)(radians/second)]
at  60Hz, 90/second [(/2)(radians/second)] at  200Hz, and
180/second [()(radians/second)] at  400Hz.
b.
Randomize the order of angular velocity used and provide sufficient rest
between trials to minimize the influence of fatigue.
Results:
The Results are the responses to the statements that follow. They are to be written in a
scientific format. You should develop figures, graphs, and spreadsheet tables to make the
results easy to read. Also, include and label graphs generated as output from the APAS
system to highlight how you obtained your results. Your format should differ from the
normal scientific format in that you must show your work (i.e., how you calculated the
results). If there are several iterations of the same calculation process, you only need to
show the first to demonstrate your understanding.
Experiment 1
1.
Calculate the moments associated with anthropometric characteristics of the
subject for knee angles of 165, 150, 135, 120, 105, and 90. Note that
you will need to make some assumptions about the location of the center of
mass of the foot in the plantar flexed position.
2.
Determine the moments of the shank and foot segments (multi-segment
system) for both the isometric and isokinetic conditions for knee angles of
165, 150, 135, 120, 105, and 90. Show your work. [Note that you
should use the APAS output data from Experiment 1 and subtract the
moments associated with the mechanical arm of the isokinetic dynamometer
for each corresponding angle. Take into consideration that there is an offset
between the arm of the isokinetic dynamometer and the orientation of the
shank.] Plot the calculated moments from the anthropometric method and the
two sets of moments from the isokinetic dynamometer data to show
similarities/discrepancies.
Experiments 2 and 3 [***Since the magnitude of the moments associated with the
mechanical arm of the isokinetic dynamometer is relatively small in comparison to the
moments generated during isometric and isokinetic contractions, ignore moments
associated with the weight of the arm of the isokinetic dyanmometer for Experiments 2
and 3.]
1.
Calculate Fc, Fx, OI, 1, F1, and Fy for the recorded torque values of the
isometric and isokinetic contractions and the geometry of the Hypothetical
Model for knee angles (2) of 165, 150, 135, 120, 105, and 90. Show
your work and display the results in a table. Prepare plots of the table values
to facilitate understanding.
2.
Calculate the power generated at the knee angles (2) of 165, 150, 135,
120, 105, and 90 for the angular velocities of 30/second
[(/6)(radians/second)], 90/second [(/2)(radians/second)], and
180/second [()(radians/second)]. Show your work and display the
results in a table. Prepare plots of the table values to facilitate understanding.
Note that power = moment (in Nm) X angular velocity (in radians/second).
3.
Calculate the mechanical advantage of the line of pull of the hamstring
muscles in the Hypothetical Model, relative to the knee joint center, for knee
joint angles of 165, 150, 135, 120, 105, and 90.
Discussions and Conclusions
The Discussions and Conclusions are the responses to the statements and questions that
follow. They are to be written in a scientific format.
1.
Display Results 1. in a labeled table and in plots.
What are the reasons for the discrepancies in the moment values for the
knee joint angles of 165, 150, 135, 120, 105, and 90 values as
measured by the three methods?
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.
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
3.
4.
5.
6.
7.
8.
9.
component (F1) 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.
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-velocity relationships justify these
results? Explain.
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.
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.
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.
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 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?
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.
*CALIBRATION PROCEDURES FOR VOLTAGE SIGNALS
1.
2.
3.
4.
Obtain at least two known magnitudes of the quantity (e.g., torque, angle) to be
measured. The range of magnitudes selected should represent the range of expected
experimental values.
Obtain the voltage signal from at least two (maximum and minimum) of the known
magnitudes.
Plot voltage versus magnitude for all known magnitudes. Hopefully, this plot will
be a line with a constant slope (i.e., linear relation) and zero volts represents zero
magnitude.. If this is not a linear relationship, complex mathematical equations
may need to be used to represent the relationship. Assuming a linear relationship,
continue with these procedures.
Establish a ratio between the known magnitudes and measured voltages. For
example:
Known magnitudes - 180, 150, 135, 120, 105, and 90 angles of the
electrogoniometer
Measured voltages – 9 volts for the 180 angle, 7.5 volts for the 150 angle,
7 volts for the 135 angle, 5.5 volts for the 120 angle, 5 volts for
the 105 angle, and 4.5 volts for the 90 angle. Note this assumes that
there are 0 volts for 0 magnitude and that there is nearly a linear
relationship between volts and angles. The relationship between volts
and angles is:
180/9V = 20/volt  a 10V signal is 200
In other words, multiply volts by 20 to obtain degrees.