© 2008 mcgraw-hill higher education. all rights reserved. chapter 10: terminology and measurement...
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© 2008 McGraw-Hill Higher Education. All Rights Reserved.
Chapter 10:Terminology and Measurement
in Biomechanics
KINESIOLOGY
Scientific Basis of Human Motion, 11th edition
Hamilton, Weimar & LuttgensPresentation Created by
TK Koesterer, Ph.D., ATC
Humboldt State University
Revised by Hamilton & Weimar
KINESIOLOGY
Scientific Basis of Human Motion, 11th edition
Hamilton, Weimar & LuttgensPresentation Created by
TK Koesterer, Ph.D., ATC
Humboldt State University
Revised by Hamilton & Weimar
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© 2008 McGraw-Hill Higher Education. All Rights Reserved.
Objectives
1. Define mechanics & biomechanics.2. Define kinematics, kinetics, statics, & dynamics, and
state how each relates to biomechanics. 3. Convert units of measure; metric & U.S. system.4. Describe scalar & vector quantities, and identify.5. Demonstrate graphic method of the combination &
resolution of two-dimensional (2D) vectors. 6. Demonstrate use of trigonometric method for
combination & resolution of 2D vectors.7. Identify scalar & vector quantities represented in
motor skill & describe using vector diagrams.
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Mechanics
• Area of scientific study that answers the questions, in reference to forces and motion– What is happening?– Why is it happening?– To what extent is it happening?
• Deals with force, matter, space & time.• All motion is subject to laws and principles of
force and motion.
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Biomechanics
• The study of mechanics limited to living things, especially the human body.
• An interdisciplinary science based on the fundamentals of physical and life sciences.
• Concerned with basic laws governing the effect that forces have on the state of rest or motion of humans.
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Statics and Dynamics
• Biomechanics includes statics & dynamics.Statics: all forces acting on a body are balanced
F = 0 - The body is in equilibrium.Dynamics: deals with unbalanced forces
F 0 - Causes object to change speed or direction.
• Excess force in one direction.• A turning force.
• Principles of work, energy, & acceleration are included in the study of dynamics.
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Kinematics and Kinetics
Kinematics: geometry of motion• Describes time, displacement, velocity, &
acceleration.• Motion may be straight line or rotating.
Kinetics: forces that produce or change motion. • Linear – causes of linear motion.• Angular – causes of angular motion.
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QUANTITIES IN BIOMECHANICSThe Language of Science
• Careful measurement & use of mathematics are essential for – Classification of facts. – Systematizing of knowledge.
• Enables us to express relationships quantitatively rather than merely descriptively.
• Mathematics is needed for quantitative treatment of mechanics.
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Units of Measurement
• Expressed in terms of space, time, and mass.
U.S. system: current system in the U.S.• Inches, feet, pounds, gallons, second
Metric system: currently used in research. • Meter, kilogram, newton, liter, second
Table 10.1 present some common conversions used in biomechanics
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Units of Measurement
Length: • Metric; all units differ by a multiple of 10.• US; based on the foot, inches, yards, & miles.Area or Volume: • Metric: Area; square centimeters of meters
– Volume; cubic centimeter, liter, or meters • US: Area; square inches or feet
– Volume; cubic inches or feet, quarts or gallons
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Units of Measurement
Mass: quantity of matter a body contains.
Weight: product of mass & gravity.
Force: a measure of mass and acceleration. – Metric: newton (N) is the unit of force– US: pound (lb) is the basic unit of force
Time: basic unit in both systems in the second.
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Scalar & Vector Quantities
Scalar: single quantities – Described by magnitude (size or amount)
• Ex. Speed of 8 km/hr
Vector: double quantities– Described by magnitude and direction
• Ex. Velocity of 8 km/hr heading northwest
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VECTOR ANALYSISVector Representation
• Vector is represented by an arrow• Length is proportional to magnitude
Fig 10.1
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Vector Quantities
• Equal if magnitude & direction are equal.• Which of these vectors are equal?
A. B. C. D. E. F.
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Combination of Vectors
• Vectors may be combined be addition, subtraction, or multiplication.
• New vector called the resultant (R ).
Fig 10.2
Vector R can be achieved by different combinations.
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Combination of Vectors
Fig 10.3
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Resolution of Vectors
• Any vector may be broken down into two component vectors acting at a right angles to each other.
• The arrow in this figure may represent the velocity the shot was put.
Fig 10.1c
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Resolution of Vectors• What is the vertical
velocity (A)?• What is the horizontal
velocity (B)?• A & B are
components of resultant (R)
Fig 10.4
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Location of Vectors in Space
• Position of a point (P) can be located using– Rectangular coordinates– Polar coordinates
• Horizontal line is the x axis.• Vertical line is the y axis.
x
y
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Location of Vectors in Space
• Rectangular coordinates for point P are represented by two numbers (13,5).– 1st - number of x units– 2nd - number of y units
P=(13,5)
13
5
x
y
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Location of Vectors in Space
• Polar coordinates for point P describes the line R and the angle it makes with the x axis. It is given as: (r,) – Distance (r) of point P from origin– Angle ()
x
y
13.93
21o
P
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Location of Vectors in Space
Fig 10.5
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Location of Vectors in Space
• Degrees are measured in a counterclockwise direction.
Fig 10.6
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Graphic Resolution
• Quantities may be handled graphically:– Consider a jumper who takes off with a
velocity of 9.6 m/s at an angle of 18°.
– Since take-off velocity has both magnitude & direction, the vector may be resolved into x & y components.
– Select a linear unit of measurement to represent velocity, i.e. 1 cm = 1 m/s.
– Draw a line of appropriate length at an angle of 18º to the x axis.
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Graphic Resolution• Step 1- Use a protractor to measure
18o up from the positive x-axis.• Step 2- Set a reference length. For
example: let 1 cm = 1 m/s.• Step 3- Draw a line 9.6 cm long, at
an angle of 18° from the positive x-axis.
• Step 4- Drop a line from the tip of the line you just drew, to the x-axis.
• Step 5- Measure the distance from the origin, along the x-axis to the vertical line you just drew in step 4. This is the x component (9.13cm = 9.13 m/s).
•Step 6- Measure the length of the vertical line. This is the y-component (2.97cm = 2.97m/s).
18°
9.6 m/s
x
y
9.13 cm = 9.13 m/s
2.97 cm = 2.97 m/s
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Combination of Vectors
• Resultant vectors may be obtained graphically.
• Construct a parallelogram.• Sides are linear representation of two
vectors.• Mark a point P.• Draw two vector lines to scale, with the same
angle that exists between the vectors.
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Combination of Vectors• Construct a parallelogram for the two line
drawn.• Diagonal is drawn from point P. • Represents magnitude & direction of resultant
vector R.
Fig 10.8
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Combination of Vectorswith Three or More Vectors
• Find the R1 of 2 vectors.• Repeat with R1 as one of the vectors.
Fig 10.9
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Another Graphic Method of Combining Vectors
• Vectors added head to tail.
• Muscles J & K pull on bone E-F.
• Muscle J pulls 1000 N at 10°.
• Muscle K pulls 800 N at 40°.
Fig 10.10a
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Another Graphic Method of Combining Vectors
• 1 cm = 400 N• Place vectors in
reference to x,y. • Tail of force vector of
Muscle K is added to head of force vector of Muscles J.
• Draw line R.Fig 10.10b
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Another Graphic Method of Combining Vectors
• Measure line R & convert to N:
• 4.4 cm = 1760 N• Use a protractor to
measure angle:• Angle = 23.5°
• Not limited to two vectors. Fig 10.10b
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Graphical Combination of Vectors
• Method has value for portraying the situation.• Serious drawbacks when calculating results:
– Accuracy is difficult to control.– Dependent on drawing and measuring.
• Procedure is slow and unwieldy.• A more accurate & efficient approach uses
trigonometry for combining & resolving vectors.
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Trigonometric Resolution of Vectors
• Any vector may be resolved if trigonometric relationships of a right triangle are employed.
• Same jumper example as used earlier.
• A jumper leaves the ground with an initial velocity of 9.6 m/s at an angle of 18°.
Find:• Horizontal velocity
(Vx)
• Vertical velocity (Vy)
18o
9.6m/s
x
y
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Trigonometric Resolution of Vectors
Given: R = 9.6 m/s
= 18°
To find Value Vy:
Vy = sin 18° x 9.6m/s
= .3090 x 9.6m/s
= 2.97 m/s Fig 10.11
R
V
hyp
opp ysin
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Trigonometric Resolution of Vectors
Given: R = 9.6 m/s
= 18°
To find Value Vx:
Vx = cos 18° x 9.6m/s
= .9511 x 9.6m/s
= 9.13 m/s
R
V
hyp
adj xcos
Fig 10.11
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Trigonometric Combination of Vectors
• If two vectors are applied at a right angle to each other, the solution process is also straight-forward.– If a baseball is thrown with a vertical
velocity of 15 m/s and a horizontal velocity of 26 m/s.
– What is the velocity of throw & angle of release?
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Trigonometric Combination of Vectors
Given:
Vy = 15 m/s
Vx = 26 m/sFind: R and
Solution:
R2 = V2y + V2
x
R2 = (15 m/s)2 + (26 m/s)2 = 901 m2/s2
R = √ 901 m2/s2
R = 30 m/s Fig 10.12
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Trigonometric Combination of Vectors
Solution:
Velocity = 30 m/s
Angle = 30°
o
sm
sm
x
y
V
V
30
26
15arctan
arctan
Fig 10.12
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Trigonometric Combination of Vectors
• If more than two vectors are involved.• If they are not at right angles to each other.• Resultant may be obtained by determining
the x and y components for each vector and then summing component to obtain x and y components for the resultant.
• Consider the example with Muscle J of 1000 N at 10°, and Muscle K of 800 N at 40°.
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Muscle J
R = (1000N, 10°)
y = R sin y = 1000N x .1736
y = 173.6 N (vertical)
x = R cos x = 1000N x .9848
x = 984.8 N (horizontal)
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Muscle KR = (800N, 40°)
y = R sin y = 800N x .6428
y = 514.2 N (vertical)
x = R cos x = 800N x .7660
x = 612.8 N (horizontal)
Sum the x and y components
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Trigonometric Combination of Vectors
Given:
Fy = 687.8 N
Fx = 1597.6N
Find:
and r
Fig 10.13
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Trigonometric Combination of Vectors
Solution:
NR
NR
NNR
FFR
N
N
F
F
xy
o
x
y
1739
3025395
)6.1597()8.687(
3.23
6.1597
8.687arctan
arctan
22
222
222
Fig 10.13
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Value of Vector Analysis
• The ability to understand and manipulate the variables of motion (both vector and scalar quantities) will improve one’s understanding of motion and the forces causing it.
• The effect that a muscle’s angle of pull has on the force available for moving a limb is better understood when it is subjected to vector resolution.
• The same principles may be applied to any motion such as projectiles.
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Chapter 10:Terminology and Measurement in
Biomechanics