CHAPTER 10:CHAPTER 10:TERMINOLOGY AND TERMINOLOGY AND MEASUREMENT IN MEASUREMENT IN

BIOMECHANICSBIOMECHANICS

CHAPTER 10:CHAPTER 10:TERMINOLOGY AND TERMINOLOGY AND MEASUREMENT IN MEASUREMENT IN

BIOMECHANICSBIOMECHANICSKINESIOLOGY

Scientific Basis of Human Motion, 12th editionHamilton, Weimar & Luttgens

Presentation Created byTK Koesterer, Ph.D., ATC

Humboldt State UniversityRevised by Hamilton & Weimar

Copyright © 2012 by The McGraw-Hill Companies, Inc. All rights reserved.McGraw-Hill/Irwin

10-2

ObjectivesObjectives1. 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 use of trigonometric method for combination & resolution of 2D vectors.

6. Identify scalar & vector quantities represented in a motor skill & describe using vector diagrams.

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MechanicsMechanicsArea of scientific study that answers

the questions, in reference to forces and motionWhat 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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BiomechanicsBiomechanics

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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The Study of BiomechanicsThe Study of Biomechanics

Biomechanics

Biology Mechanics

Anatomy/Physiology

Kinematics Kinetics

emg* Motion capture*Force plate/transducer*

Structure FunctionStatics

(zero or constant

velocity)

Dynamics(acceleration)

Statics(ΣF=0)

Dynamics(ΣF≠ 0)

* Tools used to collect biomechanics data in laboratories

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Statics and DynamicsStatics 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 KineticsKinematics and Kinetics

Kinematics: geometry of motionDescribes time, displacement, velocity, &

acceleration.Motion may be in a straight line or rotating.

Kinetics: forces that produce or change motion.

Linear – motion in a line.

Angular – motion around an axis.

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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.

Quantities in Biomechanics:Quantities in Biomechanics:Mathematics is the language of science

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Units of MeasurementUnits 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

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Units of MeasurementUnits of Measurement

Length:

Metric; all units differ by a multiple of 10.There are

10 millimeters in a centimeter100 centimeters in a meter1000 meters in a kilometer

US; based on the foot, inches, yards, & miles.

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Units of MeasurementUnits of Measurement

Mass: quantity of matter a body contains.

Weight: product of mass & gravity.

Force: the product of mass times acceleration. Metric: newton (N) is the unit of forceUS: pound (lb) is the basic unit of force

Time: basic unit in both systems in the second.

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Scalar & Vector QuantitiesScalar & Vector QuantitiesScalar: single quantities

Described by magnitude (size or amount)Ex. Speed of 8 km/hr

Vector: double quantitiesDescribed by magnitude and

directionEx. Velocity of 8 km/hr heading northwest

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VECTOR ANALYSISVector RepresentationVECTOR ANALYSISVector RepresentationVector is represented by an arrow

Length is proportional to magnitude

Fig 10.1

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Vector QuantitiesVector Quantities

Equal if magnitude & direction are equal.

Which of these vectors are equal?

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

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Vector QuantitiesVector 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 VectorsCombination of VectorsVectors may be combined be addition,

subtraction, or multiplication.

New vector called the resultant (R ).

Vector R can be achieved by different combinations, but is always drawn from the tail of the first vector to the tip of the last.

Fig 10.2

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Combination of VectorsCombination of Vectors

Fig 10.3

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Resolution of VectorsResolution 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 represents the velocity of the shot.

Fig 10.1c

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Resolution of VectorsResolution of VectorsWhat is the vertical

displacement (A)?

What is the horizontal d displacement (B)?

A & B are components of resultant (R)

Fig 10.4

Resultant displacement(R )

X displacement(A)

Y displacement(B)

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Location of Vectors in SpaceLocation of Vectors in Space

Position of a point (P) can be located usingRectangular coordinatesPolar coordinates

Horizontal line is the x axis.

Vertical line is the y axis.x

y

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Location of Vectors in SpaceLocation of Vectors in Space

Rectangular coordinates for point P are represented by two numbers (13,5).1st - number of x units2nd - number of y units

P=(13,5)

13

5

x

y

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Location of Vectors in SpaceLocation of Vectors in SpacePolar 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 originAngle ()

21o

13.93P

x

y

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Location of Vectors in SpaceLocation of Vectors in Space

Fig 10.5

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Location of Vectors in SpaceLocation of Vectors in Space

Degrees are measured in a counterclockwise direction.

Fig 10.6

10-25

Trigonometric Resolution of VectorsTrigonometric Resolution of Vectors

Any vector may be resolved if trigonometric relationships of a right triangle are employed.

A soccer ball is headed 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 VectorsTrigonometric 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/sFig 10.7

R

V

hyp

opp ysin

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Trigonometric Resolution of VectorsTrigonometric Resolution of VectorsGiven: 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

cos adj

hypVxR

Fig 10.7

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Trigonometric Combination of VectorsTrigonometric Combination of Vectors

If two vectors are applied at a right angle to each other, the solution process is also straight-forward.If a volleyball is served with a vertical

velocity of 15 m/s and a horizontal velocity of 26 m/s.

What is the velocity of serve & angle of release?

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Trigonometric Combination of VectorsTrigonometric Combination of VectorsGiven:

Vy = 15 m/s

Vx = 26 m/s

Find: 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 10.8

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Trigonometric Combination of VectorsTrigonometric Combination of VectorsSolution:

Velocity = 30 m/s

Angle = 30°

o

sm

sm

x

y

V

V

30

26

15arctan

arctan

Fig 10.8

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Trigonometric Combination of VectorsTrigonometric Combination of Vectors

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)

Consider the example with Muscle J of 1000 N at 10°, and Muscle K of 800 N at 40°.

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R = (800N, 40°)

y = R sin

y = 800N x .6428

y = 514.2 N (vertical)

x = R cos

x = 800N x .7660

x = 612.8 (horizontal)

Sum the x and y components

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Summed components

Fy = 687.8 N

Fx = 1597.6N

Find:

and r Fig 10.9

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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 10.9

10-35

Value of Vector AnalysisValue of Vector AnalysisThe 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.