Table Of ContentBiomechanics in Orthodontics: Principles and Practice
Biomechanics
IN Orthodontics
PRINCIPLES AND PRACTICE
Ram S. Nanda, BDS, DDS, MS, PhD
Professor Emeritus
Department of Orthodontics
College of Dentistry
University of Oklahoma
Oklahoma City, Oklahoma
Yahya S. Tosun, DDS, PhD
Private Practice
Dubai, United Arab Emirates
Former Professor
Department of Orthodontics
University of Aegea
Izmir, Turkey
41%6
Quintessence Publishing Co, Inc
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Library of Congress Cataloguing-in-Publication Data
Nanda, Ram S., 1927-
Biomechanics in orthodontics : principles and practice / Ram S. Nanda, Yahya Tosun.
p. ; cm.
Includes bibliographical references and index.
ISBN 978-0-86715-505-1
1. Orthodontic appliances. 2. Biomechanics. I. Tosun, Yahya. II. Title.
[DNLM: 1. Biomechanics. 2. Orthodontic Appliances. 3. Malocclusion—therapy. 4.
Orthodontic Appliance Design. WU 426 N176b 2010]
RK527.N366 2010 617.
6'430284—dc22
2010013547
qb
quinkutance
book/
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Contents
Preface vii
1
Physical Principles 1
2
Application of Orthodontic Force 17
31 Analysis of Two Tooth Mechanics 55
4
Frictional and Frictionless Systems 71
51 Anchorage Control 83
6P Correction of Vertical Discrepancies 99 7
i
Correction of Transverse Discrepancies 125
81 Correction of Anteroposterior Discrepancies 133
9 I Space Closure 145
Glossary 154
Index 156
Preface
Once comprehensive diagnosis and treatment planning
have set the stage for initiating treatment procedures,
appliance design and systems have to be developed to
achieve treatment goals. Correct application of the prin-
ciples of biomechanics assists in the selection of efficient
and expedient appliance systems.
Over the last three decades, there has been an explo-
sion in the development of technology related to or-
thodontics. New materials and designs for brackets,
bonding, and wires have combined to create a nearly
infinite number of possibilities in orthodontic appliance
design. As these new materials are brought together in
the configuration of orthodontic appliances, it is neces-
sary to understand and apply the principles of biome-
chanics for a successful and efficient treatment outcome.
Lack of proper understanding may not only set up in-
efficient force systems but also cause collateral dam-
age to the tissues. The path to successful treatment is
through good knowledge of biomechanics.
This book is written with the purpose of introducing
a student of orthodontics to the evolving technology,
material properties, and mechanical principles involved
in designing orthodontic appliances.
vii
Physical Principles 7
'
70
1
Movement of teeth in orthodontic treatment requires
application of forces and periodontal tissue response to
these forces. Force mechanics are governed by physi-
cal principles, such as the laws of Newton and Hooke.
This chapter presents the basic definitions, concepts,
and applicable mechanical principles of tooth move-
ment, laying the groundwork for subsequent chapters.
Newton's Laws
Isaac Newton's (1642-1727) three laws of motion, which
analyze the relations between the effective forces on ob-
jects and their movements, are all applicable to clinical
orthodontics.
The law of inertia
The law of inertia analyzes the static balance of objects.
Every body in a state of rest or uniform motion in a
straight line will continue in the same state unless it is
compelled to change by the forces applied to it.
The law of acceleration
The law of acceleration states that the change in motion
is proportional to the motive force that is applied. Ac-
celeration occurs in the direction of the straight line in
which the force is applied: a= F/m, where a= acceler-
ation, F= force, and m = mass.
The law of action and reaction
The reaction of two objects toward each other is always
equal and in an opposite direction. Therefore, to every
action there is always an equal and opposite reaction.
1
1 i Physical Principles
Fig 1-1 Force is a vector. The force applied to the incisor is signified
by the length of the arrow, and the point of application is on the crown.
Its line of action is horizontal, and its direction is from anterior to pos-
terior.
y
x
■
1
■
4 1 1 0 .
R
b
Fig 1.2 The resultant (R) of forces (x and y) on the same line of action and direction is R = x + y (a) and the same line of action but in different
directions is R = x + (—y) (b).
Fig 1-3 (a) The resultant (R) of the x and y vectors that have the same point of origin is the diagonal of the parallelogram with these vectors used
as the sides. (b) R can also be obtained by drawing a vector parallel to vector y and extending from the tip of vector x, then drawing a line joining
its tip to the origin of vector x.
I Vectors
When any two points in space are joined, a line of action
is created between these points. When there is move-
ment from one of these points toward the other, a direc-
tion is defined. The magnitude of this force is called a
vector, it is shown by the length of an arrow, and its
point of application is shown with a point. For example,
in Fig 1-1, the line of action of the force vector, which is
applied by the labial arch of a removable appliance on
the labial surface of the crown of the incisor, is hori-
zontal. The direction is backward (ie, from anterior to
posterior), and its amount is signified by the length of
the arrow.
2
