vector algebra. course content i.introduction to the course ii.biomechanical concepts related to...
TRANSCRIPT
Course Content
I. Introduction to the CourseII. Biomechanical Concepts Related
to Human MovementIII. Anatomical Concepts Related to
Human MovementIV. Applications in Human
Movement
Vector Representation A vector quantity is
represented by an arrow.
Arrow head represents direction.
Tail represents point of forceapplication.
Line of force (or pull).
Length represents magnitude.
Force Vector
Examples of Vector Representations
Luttgens & Hamilton. (2001). Fig 10.1. p. 266.
Luttgens & Hamilton. (2001). Fig 10.1. p. 266.
Muscle Force Vectors
Point of application
Direction Magnitude Line of force
Source: Mediclip. (1995). Baltimore: Williams & Wilkins.
Vector Composition Process of determining a
resultant vector from two or more vectors
New vector called the resultant (R)
Vector Composition: Graphical Solution (Chaining)
From: LeVeau, B.F. (1992). William & Lissner’s biomechanics of human motion (3rd ed). Philadelphia: W.B. Saunders. Fig. 4-3. p. 63.
1. Select a vector to start with and draw it, maintaining direction and magnitude.
Vector Composition: Graphical Solution (Chaining)
From: LeVeau, B.F. (1992). William & Lissner’s biomechanics of human motion (3rd ed). Philadelphia: W.B. Saunders. Fig. 4-3. p. 63.
2. Chain the tail of the next vector to the head of the first, maintaining direction and magnitude from original vector.
Vector Composition: Graphical Solution (Chaining)
From: LeVeau, B.F. (1992). William & Lissner’s biomechanics of human motion (3rd ed). Philadelphia: W.B. Saunders. Fig. 4-3. p. 63.
3. Continue to chain vectors in this manner until they are all chained.
Vector Composition: Graphical Solution (Chaining)
From: LeVeau, B.F. (1992). William & Lissner’s biomechanics of human motion (3rd ed). Philadelphia: W.B. Saunders. Fig. 4-3. p. 63.
4. Draw in the resultant vector by connecting the tail of the first vector in the chain to the head of the last vector in the chain.
Vector Composition: Graphical Solution (Chaining)
5. The head of the resultant vector will be the end that is connected to the head of the last vector.
From: LeVeau, B.F. (1992). William & Lissner’s biomechanics of human motion (3rd ed). Philadelphia: W.B. Saunders. Fig. 4-3. p. 63.
Vector Composition: Graphical Solution (Chaining)
Vector P = 50 N
What is the magnitude of the resultant vector?
From: LeVeau, B.F. (1992). William & Lissner’s biomechanics of human motion (3rd ed). Philadelphia: W.B. Saunders. Fig. 4-3. p. 63.
Order of chaining does not matter.
D
R
Hamilton & Luttgens. (2001). Fig 10.2. p. 267.
If A=50 N of force, what would you estimate the magnitude of R to be?How would you state the direction of R?
A
C
B
0°
70°
The same R can be achieved from an infinite combination of vectors.
Hamilton & Luttgens. (2001). Fig 10.2. p. 267.
Magnitude of R is dependent on direction of components, not just magnitude.
If F=300 N of force, what would you estimate the magnitude of R to be?How would you state the direction of R?
From: LeVeau, B.F. (1992). William & Lissner’s biomechanics of human motion (3rd ed). Philadelphia: W.B. Saunders. Fig. 4-6. p. 64.
From: LeVeau, B.F. (1992). William & Lissner’s biomechanics of human motion (3rd ed). Philadelphia: W.B. Saunders. Fig. 4-12. p. 69.
If Q=50 N of force, what would you estimate the magnitude of R to be?
How would you state the direction of R?
From: LeVeau, B.F. (1992). William & Lissner’s biomechanics of human motion (3rd ed). Philadelphia: W.B. Saunders. Fig. 4-13. p. 69.
There is an infinite # of combinations of component vectors for any given R.
8 = 4 + 4 8 = 3 + 1 + 2 + 2 8 = 10 + (-2) 8 = 1.5 + 6.5
So, how do we know which components to resolve for?
2D (3D conceptually)
Orthogonal Horizontal &
Vertical Exceptions
Muscles Other
From: LeVeau, B.F. (1992). William & Lissner’s biomechanics of human motion (3rd ed). Philadelphia: W.B. Saunders. Fig. 4-33. p. 79.
Vector Resolution:Graphical Solution Draw a
rectangle which includes R as the diagonal of the rectangle.
From: LeVeau, B.F. (1992). William & Lissner’s biomechanics of human motion (3rd ed). Philadelphia: W.B. Saunders. Fig. 4-33. p. 79.
Hamilton & Luttgens. (2001). Fig 10.1. p. 266.
Why might you want to do this?
Vh or Vx
Vv or Vy
If Vr was 200 m/s, what is the magnitude of Vv and Vh?
Resolving Muscle Force Vectors
Direction of resolution is in direction of interest.
In this case, movement of shoulder girdle is vertical (elevation & depression) and horizontal (protraction & retraction).
Source: Mediclip. (1995). Baltimore: Williams & Wilkins.
Resolving Muscle Force Vectors
1. Draw line of pull.2. Draw vertical
component.3. Draw horizontal
component.4. Complete rectangle to
assure proper magnitudes of components.
Source: Mediclip. (1995). Baltimore: Williams & Wilkins.
1. Draw line of pull.2. Draw vertical
component.3. Draw horizontal
component.4. Complete rectangle to
assure proper magnitudes of components.
What are the linear effects produced by this muscle?
Source: Mediclip. (1995). Baltimore: Williams & Wilkins.
1. Draw line of pull.2. Draw vertical
component.3. Draw horizontal
component.4. Complete rectangle to
assure proper magnitudes of components.
Source: Mediclip. (1995). Baltimore: Williams & Wilkins.
1. Draw line of pull.2. Draw vertical
component.3. Draw horizontal
component.4. Complete rectangle to
assure proper magnitudes of components.
If the resultant force is 100 N, how much force is acting to elevate the scapula? To retract the scapula?
Source: Mediclip. (1995). Baltimore: Williams & Wilkins.
Resolving Muscle Force Vectors
1. Draw a line to represent the mechanical axis of the bone.
Source: Mediclip. (1995). Baltimore: Williams & Wilkins.
Fnormal
2. Draw in the normal component first.
Source: Mediclip. (1995). Baltimore: Williams & Wilkins.
Fnormal
Ftangential
3. Draw in the tangential component second.
Source: Mediclip. (1995). Baltimore: Williams & Wilkins.
Fnormal
Ftangential
4. Complete the rectangle to make sure that you have the lengths of your component vectors correct.
Source: Mediclip. (1995). Baltimore: Williams & Wilkins.
Fnormal
Ftangential
How would you express the direction of the resultant muscle force? The components?
Source: Mediclip. (1995). Baltimore: Williams & Wilkins.
0°
Fnormal
Ftangential
What are the linear effects produced by this muscle?
Source: Mediclip. (1995). Baltimore: Williams & Wilkins.
Fnormal
Ftangential
If the resultant muscle force is 500 N, what is the magnitude of the components?
Source: Mediclip. (1995). Baltimore: Williams & Wilkins.
From: LeVeau, B.F. (1992). William & Lissner’s biomechanics of human motion (3rd ed). Philadelphia: W.B. Saunders. Fig. 4-30. p. 77.
1. Draw a line to represent the mechanical axis of the bone.
From: LeVeau, B.F. (1992). William & Lissner’s biomechanics of human motion (3rd ed). Philadelphia: W.B. Saunders. Fig. 4-30. p. 77.
2. Draw in the normal component first.
Fnormal
From: LeVeau, B.F. (1992). William & Lissner’s biomechanics of human motion (3rd ed). Philadelphia: W.B. Saunders. Fig. 4-30. p. 77.
3. Draw in the tangential component second.
Ftangential
Fnormal
From: LeVeau, B.F. (1992). William & Lissner’s biomechanics of human motion (3rd ed). Philadelphia: W.B. Saunders. Fig. 4-30. p. 77.
4. Complete the rectangle to make sure that you have the lengths of your vectors correct.
Ftangential
Fnormal
From: LeVeau, B.F. (1992). William & Lissner’s biomechanics of human motion (3rd ed). Philadelphia: W.B. Saunders. Fig. 4-30. p. 77.
Ftangential
Fnormal
How would you express the direction of the resultant muscle force? The components?
0
Fnormal
Ftangential
Fnormal
Ftangential
Component magnitudes vary, depending on magnitude & direction of R.
Fv
From: LeVeau, B.F. (1992). William & Lissner’s biomechanics of human motion (3rd ed). Philadelphia: W.B. Saunders. Fig. 4-28. p. 75.
From: LeVeau, B.F. (1992). William & Lissner’s biomechanics of human motion (3rd ed). Philadelphia: W.B. Saunders. Fig. 4-29. p. 76.
Differences in normal component?
From: LeVeau, B.F. (1992). William & Lissner’s biomechanics of human motion (3rd ed). Philadelphia: W.B. Saunders. Fig. 4-29. p. 76.
Differences in tangential component?
Differences in muscle insertion angle?
From: LeVeau, B.F. (1992). William & Lissner’s biomechanics of human motion (3rd ed). Philadelphia: W.B. Saunders. Fig. 4-31. p. 77.
From: LeVeau, B.F. (1992). William & Lissner’s biomechanics of human motion (3rd ed). Philadelphia: W.B. Saunders. Fig. 4-32. p. 78.
From: LeVeau, B.F. (1992). William & Lissner’s biomechanics of human motion (3rd ed). Philadelphia: W.B. Saunders. Fig. 4-36. p. 82.