CHAPTER 13:CHAPTER 13:THE CONDITIONS OF THE CONDITIONS OF

ROTARY MOTIONROTARY MOTION

CHAPTER 13:CHAPTER 13:THE CONDITIONS OF THE CONDITIONS OF

ROTARY MOTIONROTARY MOTION

KINESIOLOGYScientific Basis of Human Motion, 12th edition

Hamilton, Weimar & LuttgensPresentation Created by

TK Koesterer, Ph.D., ATCHumboldt State University

Revised by Hamilton & Weimar

Copyright © 2012 by The McGraw-Hill Companies, Inc. All rights reserved.McGraw-Hill/Irwin

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ObjectivesObjectives

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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ObjectivesObjectives

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 ForceEccentric ForceRotary ForceEccentric 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 ForceExamples of Eccentric Force

Fig 13.1

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Torque 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 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 ArmLength 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.

Fig 13.4

W

d

W

d

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Torque in Rotating SegmentsTorque 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 VectorsMuscle 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 TorquesSummation of TorquesThe 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 CoupleForce Couple

The effect of equal parallel forces acting in opposite direction.

Fig 13.6 & 13.7

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Principle of TorquesPrinciple 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 directionClockwise torques are traditionally

considered to be negative.Counterclockwise torques are traditionally

considered to be positive.

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Summation of TorquesSummation of TorquesNegative Torques

(-5N x 1.5m) = (–10N x 3m) = -37.5 Nm

Positive Torque5N x 3m = 15 Nm

Resultant Torque -37.5Nm + 15Nm = -22.5 Nm

Fig 13.8

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The LeverThe 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 LeversExternal 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 LeversAnatomical LeversNearly 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 ArmsLever ArmsPortion 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 LeversClassification of Levers

Three points on the lever have been identified1. Fulcrum2. Effort force point of application3. Resistance force point of 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 LeverFirst-Class Lever

RE A

Fig 13.12

E = EffortA = Axis or fulcrumR = Resistance

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First-Class LeverFirst-Class LeverCan 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.

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Second-Class LeverSecond-Class Lever

R

EA

Fig 13.13

E = EffortA = Axis or fulcrumR = Resistance

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Second-Class LeversSecond-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 LeverThird-Class Lever

R

EA

E = EffortA = Axis or fulcrumR = Resistance Fig 13.14

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Third-Class LeversThird-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 LeversThe 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 LeversRelation of Speed to Range in Movements of LeversIn angular movements, speed and

range are interdependent.

Fig 13.18

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Selection of LeversSelection of LeversSkill 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 LeversSelection 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 LeversMechanical Advantage of LeversAbility to magnify force.

The “output” relative to its “input”.

Ratio of resistance overcome to effort applied.

Since the balanced lever equation is,

Then

MA R

E

R

EEA

RA

MA EA

RA

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Identification and Analysis of LeversIdentification 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?

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Identification and Analysis of LeversIdentification 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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Newtons’ Laws & Rotational EquivalentsNewtons’ 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.

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Moment of Inertia Moment of Inertia

Depends on:quantity of the rotating mass.its distribution around the axis of

rotation.I = mr2

M = massr = perpendicular distance between the

mass particle and the axis of rotation.

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Moment of InertiaMoment of Inertia

Fig 13.21

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Inertia in the Human BodyInertia in the Human BodyBody position affects mass distribution, and

therefore inertia.

Fig 13.22

Inertia is greater with arms outstretched

Slower Faster

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Acceleration of Rotating BodiesAcceleration of Rotating Bodies

The rotational equivalent of F = ma:

T = IT = 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 MomentumAngular 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 MomentumConservation of Angular MomentumThe 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 ReactionAction 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

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Transfer of MomentumTransfer 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 ForcesCentripetal 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):

Fcmv 2

r

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The Analysis of Rotary MotionThe Analysis of Rotary MotionAs 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 MotionGeneral Principles of Rotary Motion

The following principles need to be considered when analyzing rotary motion:TorqueSummation of TorquesConservation of Angular MomentumPrinciple of LeversTransfer of Angular Momentum