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