Transcript 10.hamilton11e_ppt_13

Chapter 13:
The Conditions of
Rotary Motion
KINESIOLOGY
Scientific Basis of Human Motion, 11th edition
Hamilton, Weimar & Luttgens
Presentation Created by
TK Koesterer, Ph.D., ATC
Humboldt State University
Revised by Hamilton & Weimar
© 2008 McGraw-Hill Higher Education. All Rights Reserved.
Objectives
1. Name, define, and use terms related to rotary
motion.
2. Solve simple lever torque problems involving
the human body and the implements it uses.
3. Demonstrate an understanding of the
effective selection of levers.
4. Explain the analogous kinetic relationships
that exist between linear and rotary motion.
5. State Newton’s laws of motion as they apply
to rotary motion.
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Objectives
6. Explain the cause and effect relationship
between the forces responsible for rotary
motion and the objects experiencing the
motion.
7. Define centripetal and centrifugal force, and
explain the relationships between these
forces and the factors influencing them.
8. Identify the concepts of rotary motion that are
critical elements in the successful
performance of a selected motor skill.
9. Using the concepts that govern motion,
perform a mechanical analysis of a selected
motor skill.
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ROTARY FORCE
Eccentric Force
 When the direction of force is not in line with
object’s center of gravity, a combination of
rotary and translatory motion is likely to occur.
 An object with a fixed axis rotates when force
is applied “off center”.
 Eccentric force: a force whose direction is not
in line with the center of gravity of a freely
moving object or the center of rotation of an
object with a fixed axis of rotation.
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Examples of Eccentric Force
Fig 13.1
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Torque
 The turning effect of an
eccentric force.
 Equals the product of the force
magnitude and the length of
the moment arm.
 Moment arm is the
perpendicular distance from
the line of force to the axis of
rotation.
 Torque may be modified by
changing either force or
moment arm.
Fig 13.2
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Length of Moment Arm
 Perpendicular
distance from the line
of force to the axis of
rotation.
 The moment arm is
no longer the length
of the forearm.
 Can be calculated
using trigonometry.
Fig 13.3
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Length of Moment Arm
 In the body, weight of
a segment cannot be
altered
instantaneously.
 Therefore, torque of a
segment due to
gravitational force can
be changed only by
changing the length of
the moment arm.
d
Fig 13.4
W
d
W
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Torque in Rotating Segments
 Muscle forces that exert torque are
dependent on point of insertion of the
muscle, & changes in length, tension,
and angle of pull.
Fig 13.5
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Muscle Force Vectors
 Only the rotary component is actually a
factor in torque production.
 The stabilizing component acts along
the mechanical axis of the bone,
through the axis of rotation.
 Thus, it is not eccentric, or off-center.
 The moment arm length is equal to zero.
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Summation of Torques
 The sum of two or more torques may
result in no motion, linear motion, or
rotary motion.
– Parallel eccentric forces applied in the
same direction on opposite sides of the
center of rotation; Ex. a balanced seesaw.
– If equal parallel forces are adequate to
overcome the resistance, linear motion will
occur; Ex. paddlers in a canoe.
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Force Couple
 The effect of equal parallel forces acting
in opposite direction.
Fig 13.6 & 13.7
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Principle of Torques
 Resultant torques in a force system must be
equal to the sum of the torques of the
individual forces of the system about the
same point.
 Must consider both magnitude and direction
– Clockwise torques are traditionally considered to
be negative.
– Counterclockwise torques are traditionally
considered to be positive.
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Summation of Moments
Negative Moments:
(-5N x 1.5m) = (-10N x 3m) = -37.5 Nm
Positive moment: 5N x 3m = 15 Nm
Resultant moment: -37.5Nm + 15Nm = -22.5 Nm
Fig 13.8
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THE LEVER
 A rigid bar that can rotate about a fixed
point when a force is applied to
overcome a resistance.
 They are used to:
– Balance 2 or more forces.
– Favor force production.
– Favor speed and range of motion.
– Change the direction of the applied force.
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External Levers
 Using a small force to overcome a large
resistance.
 Ex. a crowbar
 Using a large ROM to overcome a small
resistance.
 Ex. Hitting a golf ball
 Used to balance a force and a load.
 Ex. a seesaw
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Anatomical Levers




Nearly every bone is a lever.
The joint is the fulcrum.
Contracting muscles are the force.
Do not necessarily resemble bars.
 Ex. skull, scapula, vertebrae
 The resistance point may be difficult to
identify.
 May be difficult to determine resistance.
 weight, antagonistic muscles & fasciae.
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Lever Arms
 Portion of lever between




fulcrum & force
application.
Effort arm (EA):
Perpendicular distance
between fulcrum & line
of force of effort.
Resistance arm (RA):
Perpendicular distance
between fulcrum & line
of resistance force.
Fig 13.16
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Classification of Levers
 Three points on the lever have been identified
 1. Fulcrum
 2. Effort force application
 3. Resistance force application
 There are three possible arrangements of
these points.
 This arrangement is the basis for the
classification of levers.
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First-Class Lever
R
E
A
E = Effort
A = Axis or fulcrum
R = Resistance
Fig 13.12
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First-Class Lever
• Can be used to achieve all four functions
of a simple machine.
• Depends on relative lengths of effort arm
and resistance arm:
– Balance 2 or more forces:
• If effort force and resistance force are equal, effort arm and resistance arm
are equal.
– Favor force production:
• If effort force and resistance force are equal, effort arm is longer than the
resistance arm.
– Favor speed and range of motion:
• If effort force and resistance force are equal, resistance arm is longer than
the effort arm.
– Change direction of applied force:
• If you push down on one side of a seesaw, the other side goes up.
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Second-Class Lever
R
A
E
E = Effort
A = Axis or fulcrum
R = Resistance
Fig 13.13
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Second-Class Levers
 Primary function is to magnify the effect
of force production.
 The effort arm is always longer than the
resistance arm.
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Third-Class Lever
R
A
E
E = Effort
A = Axis or fulcrum
R = Resistance
Fig 13.14
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Third-Class Levers
 Primary function is to magnify speed
and range of motion.
 Resistance arm is longer than effort arm
– so even though the entire lever will
move through the same angular
distance, the effort moves a small linear
distance, while the resistance moves
through a larger linear distance.
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The Principle of Levers
Any lever will balance when the product of
the effort and the effort arm equals the
product of the resistance and the
resistance arm.
E x EA = R x RA
Fig 13.16
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Relation of Speed to Range in
Movements of Levers
 In angular movements, speed and
range are interdependent.
Fig 13.18
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Selection of Levers
 Skill in motor performance depends on
the effective selection and use of levers,
both internal and external.
Fig 13.19
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Selection of Levers
 It is not always desirable to choose the
longest lever arm.
– Short levers enhance angular velocity,
while sacrificing linear speed and range of
motion.
– Strength needed to maintain angular
velocity increases as the lever lengthens.
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Mechanical Advantage
of Levers
 Ability to magnify force.
 The “output” relative to its “input”.
 Ratio of resistance overcome to effort
applied.
 MA = R / E
 Since the balanced lever equation is,
 R / E = EA / RA
 Then MA = EA / RA
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Identification and
Analysis of Levers
For every lever these questions should be
answered:
1. Where are fulcrum, effort application &
resistance application?
2. At what angle is the effort applied to the
lever?
3. At what angle is the resist applied to the
lever?
4. What is the effort arm of the lever?
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Identification and
Analysis of Levers
5. What is the resistance arm of the lever?
6. What are the relative lengths of the effort
& resistance arms?
7. What kind of movement does this lever
favor?
8. What is the mechanical advantage?
9. What class of lever is this?
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NEWTON’S LAWS AND
ROTATIONAL EQUIVALENTS
1. A body continues in a state of rest or uniform
rotation about its axis unless acted upon by
an external force.
2. The acceleration of a rotating body is directly
proportional to the torque causing it, is in the
same direction as the torque, and is inversely
proportional to moment of inertia of the body.
3. When a torque is applied by one body to
another, the second body will exert an equal
and opposite torque on the first.
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Moment of Inertia
• Depends on:
– quantity of the rotating mass.
– its distribution around the axis of rotation.
I = mr2
M = mass
r = perpendicular distance between the mass
particle and the axis of rotation.
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Moment of Inertia
Fig 13.21
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Inertia in the Human Body
 Body position affects mass distribution,
and therefore inertia.
Fig 13.22
Slower
Faster
Inertia 3 times greater with arms
outstretched.
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Acceleration of Rotating Bodies
 The rotational equivalent of F = ma:
 T = I
 T = torque, I = moment of inertia,  =
angular acceleration
 Change in angular acceleration () is
directly proportional to the torque (T) and
inversely proportional to the moment of
inertia (I):

=T/I
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Angular Momentum
 The tendency to persist in rotary motion.
 The product of moment of inertia (I) and
angular velocity ():
 Angular momentum = I
• Can be increased or decreased by
increasing either the angular velocity or
the moment of inertia.
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Conservation of
Angular Momentum
The total angular momentum of a rotating
body will remain constant unless acted
upon by an external torque.
 A decrease in I produces an increase in :
Fig 13.23
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Action and Reaction
 Any changes is the moments of
inertia or velocities of two
bodies will produce equal and
opposite momentum changes.
I (vf1 - vi1) = I (vf2 - vi2)
Fig 13.24
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Transfer of Momentum
 Angular momentum
may be transferred
from one body part to
another as the total
angular momentum
remains unaltered.
 Angular momentum
can be transferred into
linear momentum, and
vice versa.
Fig 13.25
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CENTRIPETAL AND
CENTRIFUGAL FORCES
Centripetal force: a constant center-seeking force
that acts to move an object tangent to the
direction in which it is moving at any instant,
thus causing it to move in a circular path.
Centrifugal force: an outward-pulling force equal
in magnitude to centripetal force.
Equation for both (equal & opposite forces):
Fc = mv2 / r
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THE ANALYSIS OF
ROTARY MOTION
 As most motion of the human body involves
rotation of a segment about a joint, any
mechanical analysis of movement requires an
analysis of the nature of the rotary forces, or
torques involved.
– Internal torques by applied muscle forces.
– External torques must be identified as they are
produced in the analysis of linear motion.
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General Principles
of Rotary Motion
 The following principles need to be
considered when analyzing rotary
motion:
– Torque
– Summation of Torques
– Conservation of Angular Momentum
– Principle of Levers
– Transfer of Angular Momentum
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Chapter 13:
The Conditions of
Rotary Motion
© 2008 McGraw-Hill Higher Education. All Rights Reserved.