ENBI 3510/4510: Intro to Biomechanics HW #2 Spring 2021 Dr. Chadd Clary Page 1 of 3 Due Date: Submit to Canvas on April 20th, 2021 by 11:59 PM. Part 1: 3D Knee Kinematic Descriptions Problem Statement: A subject’s femur, tibia, and fibula were segmented from a CT scan in the supine position (laying down). The segmented bones are located in the global (CT scanner) coordinate system. In addition, anatomic landmarks on the femur and tibia were identified that can be used to build anatomic femoral and tibial coordinate systems using the methods described in class. Your task is to build these coordinate systems, construct the transformation matrix describing the orientation of the femur coordinate system in the tibial anatomic coordinate system, and calculate the Grood & Suntay kinematics of the knee’s 3D orientation. The raw data and additional details can be found in Canvas on the Homework #2 page: • Homework_2_Part1_Intro.m (data introduction and description) • KNEE.mat (raw data, keep in same folder as the .m file) Detailed Steps: 1. Calculate the Femoral Anatomic Coordinate system using the anatomic landmarks as follows: a. The femoral origin is located at the most distal point in the trochlear groove. b. The S-I vector is from the femoral origin to the center of the femoral head. c. The temporary M-L vector from the medial epicondyle to the lateral epicondyle, pointing laterally. d. The A-P vector is the cross product of the S-I vector and the temporary M-L vector, pointing anteriorly. e. The M-L vector is the cross product of the A-P and S-I vector, pointing laterally. 2. Calculate the Tibial Anatomic Coordinate system using the anatomic landmarks as follows: a. The centers of the medial and lateral tibial plateaus should be calculated as the mid- points between the most anterior and most posterior points on each plateau, respectively. b. The tibial origin is the mid-point between the centers of the medial and lateral plateaus. c. The S-I vector is from the ankle center to the tibial origin, pointing superiorly. d. The temporary M-L vector is from the center of the medial plateau to the center of the lateral plateau, pointing laterally. e. The A-P vector is the cross product of the S-I vector and the temporary M-L vector, pointing anteriorly. f. The M-L vector is the cross product of the A-P and S-I vector, pointing laterally. 3. Transform the femoral anatomic coordinate system into the tibial anatomic coordinate system. 4. Calculate the Grood & Suntay knee kinematic from the tibia-femur transformation matrix. 5. Additional steps for the Graduate Section of the class: KNEE.mat also contains a series of tibia- femur transformation matrices that describe the knee movement during a deep knee bending activity. Calculate the G&S kinematics for the entire movement. Generate a plot of the relative orientation of the femur and tibia at the moment in the activity ...

1. ENBI 3510/4510: Intro to Biomechanics HW #2
Spring 2021 Dr. Chadd Clary
Page 1 of 3
Due Date: Submit to Canvas on April 20th, 2021 by 11:59 PM.
Part 1: 3D Knee Kinematic Descriptions
Problem Statement: A subject’s femur, tibia, and fibula were
segmented from a CT scan in the supine
position (laying down). The segmented bones are located in the
global (CT scanner) coordinate system.
In addition, anatomic landmarks on the femur and tibia were
identified that can be used to build
anatomic femoral and tibial coordinate systems using the
methods described in class. Your task is to
build these coordinate systems, construct the transformation
matrix describing the orientation of the
femur coordinate system in the tibial anatomic coordinate
system, and calculate the Grood & Suntay
kinematics of the knee’s 3D orientation.
The raw data and additional details can be found in Canvas on
the Homework #2 page:

2. • Homework_2_Part1_Intro.m (data introduction and
description)
• KNEE.mat (raw data, keep in same folder as the .m file)
Detailed Steps:
1. Calculate the Femoral Anatomic Coordinate system using the
anatomic landmarks as follows:
a. The femoral origin is located at the most distal point in the
trochlear groove.
b. The S-I vector is from the femoral origin to the center of the
femoral head.
c. The temporary M-L vector from the medial epicondyle to the
lateral epicondyle,
pointing laterally.
d. The A-P vector is the cross product of the S-I vector and the
temporary M-L vector,
pointing anteriorly.
e. The M-L vector is the cross product of the A-P and S-I
vector, pointing laterally.
2. Calculate the Tibial Anatomic Coordinate system using the
anatomic landmarks as follows:
a. The centers of the medial and lateral tibial plateaus should be
calculated as the mid-

3. points between the most anterior and most posterior points on
each plateau,
respectively.
b. The tibial origin is the mid-point between the centers of the
medial and lateral plateaus.
c. The S-I vector is from the ankle center to the tibial origin,
pointing superiorly.
d. The temporary M-L vector is from the center of the medial
plateau to the center of the
lateral plateau, pointing laterally.
e. The A-P vector is the cross product of the S-I vector and the
temporary M-L vector,
pointing anteriorly.
f. The M-L vector is the cross product of the A-P and S-I
vector, pointing laterally.
3. Transform the femoral anatomic coordinate system into the
tibial anatomic coordinate system.
4. Calculate the Grood & Suntay knee kinematic from the tibia-
femur transformation matrix.
5. Additional steps for the Graduate Section of the class:
KNEE.mat also contains a series of tibia-
femur transformation matrices that describe the knee movement
during a deep knee bending

4. activity. Calculate the G&S kinematics for the entire
movement. Generate a plot of the relative
orientation of the femur and tibia at the moment in the activity
when the knee is flexed to 45°.
ENBI 3510/4510: Intro to Biomechanics HW #2
Spring 2021 Dr. Chadd Clary
Page 2 of 3
Part 2: Inverse dynamics
Problem Statement: Lecture 5, we solved for the ankle
forces and moments of a foot pushing off from the
ground at toe-off during gait (see lecture notes). In this
problem, propagate the reaction forces and moments at
ankle onto the shank and solve for the reaction forces
and moments at the knee.
For the foot:
• Fgr,f = 150 N
• Fgr,n = 800 N

5. • mfoot = 1.4 kg
• Ifoot = 0.05 kg∙m2
• ax = 7.5 m/s2
• ay = 2 m/s2
• α = -15 rad/s2
For the shank:
• mshank = 3.4 kg
• Ishank = 0.06 kg∙m2
• ashank,x = 13 m/s2
• ashank,y = 3 m/s2
• α = -18 rad/s2

6. ENBI 3510/4510: Intro to Biomechanics HW #2
Spring 2021 Dr. Chadd Clary
Page 3 of 3
Deliverable: Provide a summary memo using the template
provided on Canvas, including…
Part 1:
• Report the tibial anatomic coordinate system
• Report the femoral anatomic coordinate system
• Include a plot of the tibia and femur in the tibial anatomic
coordinate system. Include lines
(vectors) from the origin along the x-, y-, and z-axes for
reference.
• Report the G&S kinematics of the knee pose in the CT Scan
(ML, AP, SI, FE, AA, IE).
• Write a brief discussion of how uncertainty or error in
identification of the anatomic landmarks
would influence the calculated anatomic coordinate system and
the associated tibia-femoral
kinematics.
• Additional steps for the Graduate Section of the class: Include
plots of the G&S Kinematics for

7. the flexion cycle. The first plot should show the Ad-Ab and I-E
rotational kinematics versus knee
flexion. The second plot should include the translational
kinematics (M-L, A-P, and S-I) versus
knee flexion. Include the plot of the relative orientation of the
femur and tibia at the moment in
the activity when the knee is flexed to 45° in the tibial
coordinate system.
Part 2:
• Draw the Free-body-diagram for the shank, including all
externally applied loading.
• Include your complete calculations (insert a photo of neatly
handwritten work).
• Report the reaction forces and moment at the knee.
Essay 1: How do we work with limited knowledge?
David Hume is famous for showing philosophers that we rely on
induction (or the generalization of something from specific
instances). For instance, Hume showed us that just because the
sun has been rising every day for as long as humans can
remember, that that alone provides no proof that the sun will
rise again tomorrow. Even physics, which now can describe the
motion of the universe in pretty astonishing detail, has to admit
that it can't prove that the sun will rise tomorrow. It is just
physics' "best guess".

8. This pandemic is a great example of how the world gets turned
upside down when something knew (the Coronavirus) makes us
rethink a lot of things that we held as "givens". And, as we
struggle to learn about the virus, we also struggle with the fact
that there are so many "unknowns" surrounding it.
I don't want to get into a political discussion here. The question
is simply: How do we live in a world that we have limited
knowledge about? How do we combat the skeptic that just
throws their hands up and says "It is all a big pile of BS, you
don't know anything, so don't try to tell me anything". How do
we deal with the fact that we, in fact, do often have limited
knowledge, but have to make decisions?
Again, this is not a political science class, so your
response/argument should be supported by passages from the
text (or other philosophical sources). And, as always, be
respectful to your peers.
Your initial post should be at least 3 solid paragraphs.
Remember to reference material from the text (properly) to
support your post - e.g. "as Hume said in the text concerning
_____, The case is that ____ is true"
After completing your initial post, take the time to respond to at
least two of your classmates. Please pick at least one response
from a peer that argues against your own position. In that reply
explain what about their position you think is the most
compelling (interesting)? Each reply should be at, a minimum,
a solid and substantial paragraph, or a minimum of 4 solid
sentences; however, your focus should be on relating to your
peers and not on meeting the minimum requirements to
complete the assignment.
What ethical theory do you most relate to?
Choose the major ethical theory discussed in chapter 7 that you
think is the strongest theory. Then create your post
incorporating the answers to the following questions: Why is it
the strongest theory? Why is it better than the others? What is

9. the theory's most glaring weakness? How would you respond to
that weakness?
Your initial post should be at least 3 solid paragraphs.
Remember to reference material from the text (properly) to
support your post - e.g. "as Hume said in the text concerning
_____, The case is that ____ is true". You will not be able to
see your peers' responses until you submit your own.
After completing your initial post, take the time to respond to at
least two of your classmates. Please pick at least one response
from a peer that argues against your own position. In that reply
explain what about their position you think is the most
compelling (interesting)? Each reply should be at, a minimum,
a solid and substantial paragraph, or a minimum of 4 solid
sentences; however, your focus should be on relating to your
peers and not on meeting the minimum requirements to
complete the assignment.
Discussion - Rawls
John Rawls remains one of the most respected
American philosophers in history. His arguments for social
justice are still being heard today as people protest the vast
inequalities in American society. So, for this discussion, I want
you to read Rawls closely and then pick out something he said
that "speaks to you" - in either a positive or negative way.
Then write about it, giving your take on what it means to you.
Your initial post should be at least 3 solid paragraphs.
Remember to reference material from the text (properly) to
support your post - e.g. "as Hume said in the text concerning
_____, The case is that ____ is true" Note: You will not be able
to see other student's posts until you post your own.
After completing your initial post, take the time to respond to at
least two of your classmates. Please pick at least one response
from a peer that argues against your own position. In that reply
explain what about their position you think is the most
compelling (interesting)? Each reply should be at, a minimum,

10. a solid and substantial paragraph, or a minimum of 4 solid
sentences; however, your focus should be on relating to your
peers and not on meeting the minimum requirements to
complete the assignment.