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SPEX201
Kinematics
L2 - Intro & Maths Primer
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Created by
Hailey Larsen
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Cards (19)
Adding Muscle Forces:
Muscles
contract & exert forces on bones
eg
Gluteus
maximus &
tensor
fasciae latae pull on femur
Adding Muscle Forces:
Length & direction of arrows represent force
magnitude
&
direction
(vectors)
eg Gluteus max exerting more force (
longer
arrow)
Role of gluteus max changes the force, orientation of forces important
What happens to bone from these vectors/forces?
What is their combined effect?
Body Segment Positions & Orientations:
Muscles move
body
segments
How can we describe the positions & orientations?
Landmark
positions
Centre of mass (x, y)
Difference in
coordinates
show how move body
Angles
(for orientation)
Different angles
Inside
(easy to measure)
Outside/
Supplementary
angle
Segment
angle → relative to something outside of body
Body Segment Positions & Orientations:
Landmark positions
Centre of mass on
forearm
(x, y), will be more
proximal
Elbow joint centre, talk about
distal
end (wrist joint)
Why would that be important? Difference in coordinates show how move their
body
Body Segment Positions & Orientations:
Angles (for
orientation
)
Elbow joint, where forearm is relative to upper arm
If in line = 0°
Different angles
Inside (
easy
to measure)
Outside/
Supplementary
angle
Either are fine, just say which one (need context)
Segment
angle → relative to something
outside
of body, eg vertical, laying on a bench
Use
algebra
&
trigonometry
to to calculate angles
Background:
Unit circle is centred at (0,0)
Radius is 1
Trig functions give (x, y, r) ratios
sin(50°) = 0.77 - (vertical line)
If change to 60° sin will be
bigger
as point will be higher therefore longer
cos(50°) = 0.64
If 60° it
decreases
True for
right
angle triangles
SOH-CAH-TOA:
sin(𝜃) =
o
/
h
cos(𝜃) =
a
/
h
tan(𝜃) =
o
/
a
o
pposite
side
h
ypotenuse
= longest one,
opposite
right angle
a
djacent
Depends on what you
know
& what you want to
find
Calculate the Hip Angle:
Always a
right
angle
Know
o
pposite length (22.7cm) &
a
djacent (38.9cm)
Want to find theta (𝜃)
tan
(𝜃) =
o
/
a
tan(𝜃)/tan = (o/a) / tan
𝜃 = tan(
o
/
a)
𝜃 = tan(22.7cm/38.9cm)
𝜃 = 30.3°
Calculate the Length of the Femur:
Only
opposite
& angle given
o = 22.7cm, 𝜃 = 30.3°
Want to find hypotenuse (
h
)
Needed to get h alone
sin(𝜃) = o/h
(h*sin(𝜃 ))/sin(𝜃) = o/h*(h/sin(𝜃 ))
h =
o
/
sin
(𝜃 )
h = 22.7cm/sin(30.3°)
h = 0.45m
Just the sides = Pythagorean Theorem:
a =
Vertical
distance bw/ the knee & hip joints
b =
Horizontal
distance bw/ the knee & hip joints
c =
Hypotenuse
or length of the femur
Just the sides = Pythagorean Theorem:
Right
angle triangles only, when working with
side
lengths
Those adjacent to angle = a & b doesn’t matter what is what
c = hyp,
opposite
right angle
Pythagorean Theorem:
Calculate the length of the femur:
Have a & b looking for c
c^2 =
a
^2 +
b
^2
Need to get rid of square on both sides
So
square
root
c (√c^2)
c = √a^2 + b^2
c =
√(38.9cm^2) + (22.7cm^2)
c = 0.45m
Maths used, but applications will changed
Vectors:
Vectors have
magnitude
&
direction
Can be described in terms of
vertical
(y) &
horizontal
(x) components
Vectors:
Force
plate
measures
reaction
force onto ground
Can use to determine what's gonna happen to their body?
Reaction force mostly up & anterior
Length of
arrow
& orientation tells you
interaction
with the ground
How much of this force is vertical (
up
), &
horizontal
(forward)
Make right angle triangles
Adding & Subtracting Vectors:
Segments are often subject to
many
forces, to find the overall effect we
add
them
If forces are
parallel
& act along the same line, we can add them algebraically
Solving Vector Problems:
Often need to resolve a
resultant
vector into its components
Decide on a
reference
frame for the components
Horizontal
&
vertical
relative to the ground
May not be
horizontal
or
vertical
(eg lay on bench)
Anatomical
planes
Along a
segment
&
perpendicular
to it
To a joint (segment) & perpendicular to rotate
Multiple Muscle Forces:
Find components of F1 & F2 that are
parallel
(eg to the femur)
Find components of F1 & F2 that are
perpendicular
(eg to the femur)
Find the combined (
resultant
) force of F1 & F2
Multiple Muscle Forces:
Find the combined (
resultant
) force of F1 & F2
Add
parallel
components
Fry = F1x + F2y
Fry = 1033.7 N
Add
perpendicular
components
Frx = F1x + F2x
Frx = -239.4 N + 136.8 N
Frx = -102.6 N
Fr = √Fry^2 + Frx^2
Fr = 1038.8 N
𝜃 = tan-1 Frx/Fry
𝜃 = 5.7 (posterior of long axis)