L2 - Intro & Maths Primer

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
    • opposite side
    • hypotenuse = longest one, opposite right angle
    • adjacent
    • Depends on what you know & what you want to find
  • Calculate the Hip Angle:
    • Always a right angle
    • Know opposite length (22.7cm) & adjacent (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:
    1. Find components of F1 & F2 that are parallel (eg to the femur)
    2. Find components of F1 & F2 that are perpendicular (eg to the femur)
    3. 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)