Introduction to Biomechanics and Vector Resolution

Applied Kinesiology420:151

Agenda

Introduction to biomechanics Units of measurement Scalar and vector analysis

Combination and resolution Graphic and trigonometric methods

Introduction to Biomechanics

Biomechanics

Statics Dynamics

Kinetics and Kinematics

Kinetics and Kinematics

Linear vs. Angular Linear vs. Angular

The study of biological motion

The study of forces on the body in equilibrium

The study of forces on the body subject to unbalance

Kinetics: The study of the effect of forces on the body

Kinematics: The geometry of motion in reference to time and displacement

Linear: A point moving along a line

Angular: A line moving around a point

Agenda

Introduction to biomechanics Units of measurement Scalar and vector analysis

Combination and resolution Graphic and trigonometric methods

Units of Measurement

Systeme Internationale (SI) Base units Derived units Others

SI Base Units

Length: SI unit meter (m) Time: SI unit second (s) Mass: SI unit kilogram (kg) Distinction: Mass (kg) vs. weight

(lbs.) Mass: Quantity of matter Weight: Effect of gravity on matter Mass and weight on earth vs. moon?

SI Derived Units Displacement: A change in position

SI unit m Displacement vs. distance?

Velocity: The rate of displacement SI unit m/s Velocity vs. speed?

Acceleration: The rate of change in velocity SI unit m/s/s or m/s2

SI Derived Units Force: The product of mass and

acceleration SI Unit Newton (N) The force that is able to

accelerate 1 kg by 1 m/s2

How many N of force does a 100 kg person exert while standing?

Moment: The rotary action of a force Moment = Fd SI Unit N*m When 1 N of force is applied at

a distance of 1 m away from the axis of rotation

SI Derived Units Work: The product of force and distance

SI Unit Joule (J) When 1 N of force moves through 1 m

Note: 1 J = 1 N*m Energy: The capacity to do work

SI Unit J Note: 1 J = ~ 4 kcal

Power: The rate of doing work (work/time) SI Unit Watt (W) When 1 J (or N*m) is

performed in 1 s Note: Also calculated as F*V

Deadlift Example

Other Units Area: The superficial contents or

surface within any given lines 2D in nature SI Unit m2

Volume: The amount of space occupied by a 3D structure SI Unit m3 or liter (l) Note: 1 l = 1 m3

Agenda

Introduction to biomechanics Units of measurement Scalar and vector analysis

Combination and resolution Graphic and trigonometric methods

Scalar and Vector Analysis Scalar defined: Single quantities of

magnitude no description of direction A speed of 10 m/s A mass of 10 kg A distance of 10 m

Vector defined: Double quantities of magnitude and direction A velocity of 10 m/s in forward direction A vertical force of 10 N A displacement of 10 m in easterly direction

Scalar and Vector Representation

Scalars are represented as values that represent the magnitude of the quantity

Vectors are represented as arrows that represent: The direction of the vector quantity

(where is the arrow pointing?) The magnitude of the vector (how long is

the arrow?)

Figure 10.1, Hamilton

Combination of Vectors

Vectors can be combined which results in a new vector called the resultant.

We can combine vectors three ways: Addition Subtraction Multiplication

Vector Combination: Addition

Tip to tail method The resultant vector is represented

by the distance between the tail of first vector and the tip of the second

Vector 1

+

Vector 2

=

Resultant

Vector Combination: Subtraction

Tip to tail method Resultant = Vector 1 – Vector 2 or . . .

Resultant = Vector 1 + (- Vector 2) Flip direction of negative vector

Vector 1

+

Vector 2

=

Resultant

Vector Combination: Multiplication

Tip to tail method Only affects magnitude Same as adding vectors with same

direction

X 3 =

Vector Resolution

Resolution: The breakdown of vectors into two sub-vectors acting at right angles to one another

Resultant velocity of shot at take off is a function of the horizontal

velocity (B) and the vertical velocity (A)

Location of Vectors in Space

Frame of reference: Reality = 3D 2D for simplicity

Two types: Rectangular coordinate system Polar coordinate system

Rectangular Coordinate System

Y

X

(+,+)(-,+)

(-,-) (+,-)

The vector starts at (0,0) and ends at (x,y)

Example: Vector (4,3)

Polar Coordinate System

Coordinates are (r,) where r = length of

resultant and = angle

Figure 10.5, Hamilton

Figure 10.6, Hamilton

Graphic Resolution of Vectors Tools: Graph paper, pencil, protractor Step 1: Select a linear conversion factor

Example: 1 cm = 1 m/s, 1 N or 1 m etc. Step 2: Draw in force vector based on

frame of reference Step 3: Resolve vector by drawing in

vertical and horizontal subcomponents Step 4: Carefully measure and convert

length of vectors to quantity

Assume a person performs a long jump with a take-off velocity of 5.5 m/s and a take-off angle of 18 degrees. What are the horizontal and vertical

velocities at take-off?

Conversion factor:

1 cm = 1 m

With the protractor and ruler, measure measure a vector that is 5.5 cm long with a take-off angle of 18 degrees at (0,0)

5.5 cm

5.2 cm

18 deg

1.7 cm

Horizontal velocity = 5.2 m/s

Vertical velocity = 1.7 m/s

Combination? Tip to tail method!

Trigonometric Resolution of Vectors

Advantages: Does not require precise drawing Time efficiency and accuracy

Trigonometry Terminology

Trigonometry: Measure of triangles Right triangle: A triangle that

contains an internal angle of 90 degrees (sum = 180 degrees)

Acute angle: An angle < 90 deg Obtuse angle: An angle > 90 deg

Trigonometry Terminology Hypotenuse: The side of the triangle

opposite of the right angle (longest side) Opposite leg: The side not connected to

angle in question Adjacent leg: The side connected to

angle in question (but not hypotenuse)

Angle in Q

H

O

A

Trigonometry Functions

Sine: Sine of an angle = O/H Cosine: Cosine of an angle = A/H Tangent: Tangent of an angle =

O/A

Soh Cah ToaOnline Scientific Calculator

http://www.creativearts.com/scientificcalculator

Trigonometric Resolution of Vectors

Figure 10.11, Hamilton

Trigonometric Resolution of Vectors

Pythagorean Theorum

Figure 10.12, Hamilton

Trigonometric Combination of Vectors Step 1: Resolve all vertical and

horizontal components of all vectors Step 2: Sum the vertical components

together for a new vertical component Step 3: Sum the horizontal components

for a new horizontal component Step 4: Generate new vector based on

new vertical and horizontal components

Figure 10.13, Hamilton

Figure 10.13, Hamilton

Trigonometric Combination of Several Vectors

Figure 10.14, Hamilton