CHAPTER 10:
TERMINOLOGY AND
MEASUREMENT IN
BIOMECHANICS
KINESIOLOGY
Scientific Basis of Human Motion, 12th edition
Hamilton, Weimar & Luttgens
Presentation Created by
TK Koesterer, Ph.D., ATC
Humboldt State University
Revised by Hamilton & Weimar
McGraw-Hill/Irwin
Copyright © 2012 by The McGraw-Hill Companies, Inc. 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 use of trigonometric method for
combination & resolution of 2D vectors.
6. Identify scalar & vector quantities represented in a
motor skill & describe using vector diagrams.
10-2
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.
10-3
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.
10-4
The Study of Biomechanics
Biomechanics
Biology
Mechanics
Anatomy/
Physiology
emg*
Kinematics
Force plate/
transducer*
Motion capture*
Statics
Structure
Kinetics
Function
(zero or constant
velocity)
Dynamics
Statics
(acceleration)
(ΣF=0)
Dynamics
(ΣF≠ 0)
* Tools used to collect biomechanics data in laboratories
10-5
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.
10-6
Kinematics and Kinetics
Kinematics: geometry of motion
 Describes 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.
10-7
Quantities in Biomechanics:
Mathematics is the 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.
10-8
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
10-9
Units of Measurement
Length:
 Metric; all units differ by a multiple of 10.
 There are
 10 millimeters in a centimeter
 100 centimeters in a meter
 1000 meters in a kilometer
 US; based on the foot, inches, yards, &
miles.
10-10
Units 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 force
 US: pound (lb) is the basic unit of force
Time: basic unit in both systems in the
second.
10-11
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
10-12
VECTOR ANALYSIS
Vector Representation
 Vector is represented by an arrow
 Length is proportional to magnitude
Fig 10.1
10-13
Vector Quantities
 Equal if magnitude & direction are equal.
 Which of these vectors are equal?
A.
B.
C.
D.
E.
F.
10-14
Vector Quantities
 Equal if magnitude & direction are equal.
 Which of these vectors are equal?
A.
B.
C.
D.
E.
F.
10-15
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, but is always
drawn from the tail of the first vector to the tip of the last.
10-16
Combination of Vectors
Fig 10.3
10-17
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
represents the velocity of
the shot.
Fig 10.1c
10-18
Resolution of
Vectors
Resultant displacement
(R )
Y displacement
(B)
 What is the vertical
displacement (A)?
 What is the horizontal d
displacement (B)?
X displacement
(A)
 A & B are components of
resultant (R)
Fig 10.4
10-19
Location of Vectors in Space
 Position of a point (P) can be located using
 Rectangular coordinates
y
 Polar coordinates
 Horizontal line is the x axis.
 Vertical line is the y axis.
x
10-20
Location of Vectors in Space
 Rectangular coordinates for point P are
represented by two numbers (13,5).
y
 1st - number of x units
 2nd - number of y units
P=(13,5)
5
13
x
10-21
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 ()
y
P
13.93
21o
x
10-22
Location of Vectors in Space
Fig 10.5
10-23
Location of Vectors in Space
 Degrees are measured in a counterclockwise
direction.
Fig 10.6
10-24
Trigonometric Resolution
of Vectors
y
 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°.
9.6m/s
18o
x
Find:
 Horizontal velocity (Vx)
 Vertical velocity (Vy)
10-25
Trigonometric Resolution
of Vectors
Given: R = 9.6 m/s
 = 18°
To find Value Vy:
opp Vy
sin  

hyp
R
Vy = sin 18° x 9.6m/s
= .3090 x 9.6m/s
= 2.97 m/s
Fig 10.7
10-26
Trigonometric Resolution
of Vectors
Given: R = 9.6 m/s
 = 18°
To find Value Vx:
cos  
adj
V
 x
hyp
R
Vx = cos 18° x 9.6m/s
= .9511 x 9.6m/s
= 9.13 m/s
Fig 10.7
10-27
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 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?
10-28
Trigonometric Combination
of Vectors
Given:
Vy = 15 m/s
Vx = 26 m/s
Find: R and 
Fig 10.8
Solution:
R2 = V2y + V2x
R2 = (15 m/s)2 + (26 m/s)2 = 901 m2/s2
R = √ 901 m2/s2
R = 30 m/s
10-29
Trigonometric Combination
of Vectors
Solution:
  arctan
Vy
Vx
15 m s
  arctan m
26 s
  30o
Velocity = 30 m/s
Fig 10.8
Angle = 30°
10-30
Trigonometric Combination
of Vectors
Consider the example with Muscle J of 1000 N at 10°, and Muscle K of 800 N at
40°.
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)
10-31
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
10-32
Summed
components
Fy = 687.8 N
Fx = 1597.6N
Find:
 and r
Fig 10.9
10-33
Solution:
  arctan
 Fy
 Fx
687.8 N
  arctan
1597.6 N
  23.3o
R 2   Fy2   Fx2
R 2  (687.8 N ) 2  (1597.6 N ) 2
R 2  3025395 N 2
R  1739 N
Fig 10.9
10-34
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.
10-35