chapter 10: terminology and measurement in biomechanics

© 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


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.


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.


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.


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.


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.


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.


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



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



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.


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


VECTOR ANALYSISVector Representation

• Vector is represented by an arrow• Length is proportional to magnitude

Fig 10.1


Vector Quantities

• Equal if magnitude & direction are equal.• Which of these vectors are equal?

A. B. C. D. E. F.


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.



Fig 10.3


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


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


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



• 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



• 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



Fig 10.5



• Degrees are measured in a counterclockwise direction.

Fig 10.6


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.


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



• 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.


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


Combination of Vectorswith Three or More Vectors

• Find the R1 of 2 vectors.• Repeat with R1 as one of the vectors.

Fig 10.9


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



• 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



• 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


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.


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



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



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


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?



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



Solution:

Velocity = 30 m/s

Angle = 30°

o

sm

sm

x

y

V

V

30

26

15arctan

arctan

Fig 10.12



• 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°.


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)


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



Given:

Fy = 687.8 N

Fx = 1597.6N

Find:

and r

Fig 10.13



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


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.


Chapter 10:Terminology and Measurement in

Biomechanics

chapter 10: terminology and measurement in biomechanics

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