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

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.

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.

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.

Examples of Eccentric Force Fig 13.1

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

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

Length of Moment Arm Fig 13.4 W d 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.

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

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.

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.

Force Couple The effect of equal parallel forces acting in opposite direction. Fig 13.6 & 13.7

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.

Summation of Torques Fig 13.8 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

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.

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

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.

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

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.

First-Class Lever R E A E = Effort A = Axis or fulcrum R = Resistance Fig 13.12 R E A E = Effort A = Axis or fulcrum R = Resistance

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.

Second-Class Lever R A E E = Effort A = Axis or fulcrum R = Resistance Fig 13.13 R E A E = Effort A = Axis or fulcrum R = Resistance

Second-Class Levers Primary function is to magnify the effect of force production. The effort arm is always longer than the resistance arm.

Third-Class Lever R A E E = Effort A = Axis or fulcrum R = Resistance Fig 13.14 R E A E = Effort A = Axis or fulcrum R = Resistance

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.

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

Relation of Speed to Range in Movements of Levers In angular movements, speed and range are interdependent. Fig 13.18

Selection of Levers Skill in motor performance depends on the effective selection and use of levers, both internal and external. Fig 13.19

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.

Mechanical Advantage of Levers Ability to magnify force. The “output” relative to its “input”. Ratio of resistance overcome to effort applied. Since the balanced lever equation is, Then

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?

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?

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.

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.

Moment of Inertia Fig 13.21

Inertia in the Human Body Body position affects mass distribution, and therefore inertia. Fig 13.22 Inertia is greater with arms outstretched Slower Faster

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):

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.

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

Action and Reaction I (vf1 - vi1) = I (vf2 - vi2) Fig 13.24 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)

Transfer of Momentum Fig 13.25 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.

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):

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.

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