Transcript Ch13 Powerpoint

CHAPTER 13:
THE CONDITIONS OF
ROTARY MOTION
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. 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.
13-2
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.
13-3
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.
13-4
Examples of Eccentric Force
Fig 13.1
13-5
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
13-6
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
13-7
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
W
d
W
Fig 13.4
13-8
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
13-9
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.
13-10
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.
13-11
Force Couple
 The effect of equal parallel forces acting in
opposite direction.
Fig 13.6 & 13.7
13-12
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.
13-13
Summation of Torques
Negative Torques
(-5N x 1.5m) = (–10N x 3m) = -37.5 Nm
Positive Torque
5N x 3m = 15 Nm
Resultant Torque
-37.5Nm + 15Nm = -22.5 Nm
Fig 13.8
13-14
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.
13-15
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
13-16
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.
13-17
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
13-18
Classification of Levers
 Three points on the lever have been
identified
1. Fulcrum
2. Effort force point of application
3. Resistance force point of application
 There are three possible arrangements of
these points.
 This arrangement is the basis for the
classification of levers.
13-19
First-Class Lever
R
E
A
E = Effort
A = Axis or fulcrum
R = Resistance
Fig 13.12
13-20
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:
1. Balance 2 or more forces:
 If effort force and resistance force are equal, effort arm and
resistance arm are equal.
2. Favor force production:
 If effort force and resistance force are equal, effort arm is longer
than the resistance arm.
3. Favor speed and range of motion:
 If effort force and resistance force are equal, resistance arm is
longer than the effort arm.
4. Change direction of applied force:
 If you push down on one side of a seesaw, the other side goes up.
13-21
Second-Class Lever
R
A
E
E = Effort
A = Axis or fulcrum
R = Resistance
Fig 13.13
13-22
Second-Class Levers
 Primary function is to magnify the effect of
force production.
 The effort arm is always longer than the
resistance arm.
13-23
Third-Class Lever
R
A
E
E = Effort
A = Axis or fulcrum
R = Resistance
Fig 13.14
13-24
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.
13-25
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
13-26
Relation of Speed to Range in
Movements of Levers
 In angular movements, speed and range are
interdependent.
Fig 13.18
13-27
Selection of Levers
 Skill in motor performance depends on the
effective selection and use of levers, both
internal and external.
Fig 13.19
13-28
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.
13-29
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 EA

E RA
 Then MA  EA
RA

13-30
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 resistance applied to the lever?
4. What is the effort arm of the lever?
13-31
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?
13-32
Newtons’ Laws & Rotational
Equivalents
1. A body continues is 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.
13-33
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.
13-34
Moment of Inertia
Fig 13.21
13-35
Inertia in the Human Body
 Body position affects mass distribution, and therefore
inertia.
Slower
Faster
Inertia is greater with arms outstretched
Fig 13.22
13-36
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
13-37
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.
13-38
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
13-39
Action and Reaction
 Any changes in 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
13-40
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
13-41
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):
mv
Fc 
r
2
13-42
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.
13-43
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
13-44