Week 5 Biomechanics PDF

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WEEK 5: STABILITY, MOBILITY AND BALANCE:   

Centre of gravity and how this is derived in objects and the human body. Concentric and eccentric forces. Altering the centre of gravity to produce movement.

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Introduction of rotary force: Moments and torques. Components of force.

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Equilibrium. Base of support. Balance and altering balance to produce movement.

CENTRE OF GRAVITY Body mass: The matter of which a body is composed. Body weight: The sum of all the attractive forces on a body. W= mg Weight= mass x gravity (9.81m/s/s).

Centre of mass: Mass centroid: Centre of gravity (CoG):

* The unique point around which the body’s mass is equally

distributed. * The point around which the mass and weight of a body are balanced, no matter how the body is positioned.

* The ‘Centre of Gravity’ is the most common term used. * It is the balance point of an object. *The CoG of a perfectly symmetrical the exact centre of that object.

object is

* When mass distribution within an not constant, the CoG shifts in the of the greater mass.

object is direction

* CoG can be located outside an

object.

CoG AND THE HUMAN BODY

* Every time the body changes configuration, its weight distribution and CoG location are changed. ___________________________________________________________________________ Concentric force: A force whose line of action passes through the CoG of the body on which it acts. * Causes a change in linear motion (translation in a straight line) but no changes in rotational motion. E.g. Jumping Eccentric force: A force whose line of action does though the CoG of the body on which it acts. * Causes change in rotational movement as well as in liner motion. * Initiating rotation brings in eccentric force. E.g. Sprint starting (also force couples): - Pushing of blocks. - Need CoG towards centre of shoulders. - Create instability so the body can ‘catch up’.

not pass a change

Force couple: Made up of equal, opposite and parallel forces. * Tends to cause rotation only. E.g. The crank of a bicycle. ___________________________________________________________________________ STABILITY AND BALANCE Stability: Resistance to disruption of equilibrium. * The line of gravity must project down into the base of support. E.g. Gymnastics. - Petruding leg. - Hips rotated. - Placements of shoulders. - Holding a posture is important for balance. Balance: Ability to control equilibrium. * Factors affecting balance: - Height of CoG with respect to the base of support. - The higher positioning of the CoG, the greater the potentially disruptive torque created if the body undergoes an angular displacement. - Location of the line of gravity relative to the base of support. - The closer the horizontal location of the CoG is to the boundary of the base of support, the smaller is the force required to push it outside the base of support, therefore disrupting equilibrium.

E.g. Athletes in the starting position for a race position themselves so that the CoG is close to the forward edge of the base of support (swimming/ sprinting). E.g. Sumo wrestlers lean towards their opponent when being pushed. - Mass of the athlete; According to Newton’s 2nd law of motion (F=ma), the more massive an object is, the greater is the force required to produce a given acceleration. E.g. - Rugby lineman need to be big in order to keep their position on the field despite the forces exerted on them by the opposing linesmen. - In contrast, gymnasts are at a disadvantage if they have a greater body mass, because execution of most gymnastic skills involves the disruption of stability. Base of Support: The area made with the part of the body that’s touching the supporting surface (generally the ground). * A critical variable in considering balance. * When the line of action of a body weight (directed from the CoG) moves outside the base of support, a torque is created that tends to cause angular motion of the body, therefore disrupting stability, with the CoG falling towards the ground. * Larger base of support = less likely to fall. * When teaching balance activities start with a low CoG and wide base of support. Then progress to smaller bases of support and higher CoG as confidence and skill increases. ___________________________________________________________________________ MOMENTS & TORQUES

Torque: The rotary effect created by an applied force. Moment Arm: Shortest (perpendicular) distance between and axis of rotation.

a force’s line of action

M= F.s Moment/ Torque = Force x perpendicular arm

distance/moment

* For any given muscle, the moment arm is largest when the bone is closest to 90°.

the angle of pull on

* Changes in moment arm directly affects the joint generates.

torque that a muscle

E.g. At the Elbow, as the angle of pull moves away from direction, the moment arm for the elbow flexors is progressively diminished.

90° in either

(practice questions on slides).

___________________________________________________________________________ EQUILIBRIUM * The state of a system that is not changing its speed or direction. Static equilibrium: A body at rest. Dynamic equilibrium: A body that has unchanging speed or direction. * The stability of a body/ the state of balance. Stable equilibrium: If a small perturbation (disturbance) is applied to an object, then it tends to return to its original position. - Important in hitting type sports: Get yourself into a stable position. - Wide base of support. Unstable equilibrium: If a small perturbation is applied then it tends to accelerate away from its original position. -Close to moving. Neutral equilibrium: If a small perturbation is applied then the object neither accelerates away nor returns from its original position. Stable

Unstable

Neutral

W

W

Description of body position

W

W

Description of equipment

WEEK 6: PROJECTILE MOTION: Effect of gravity on objects. Factors influencing projectiles. Analysis of projectile motion. Optimising distance of a projectile.

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KINEMATICS OF PROJECTILE MOTION Projectile: Body in free fall that is subject only to the forces of gravity and air resistance. E.g. Discus, Javelin. NOT aeroplanes and rockets as they are also influenced by the forces generated by their engines. Projectile motion: The motion of objects under the influence of gravity. It is characterised by constant horizontal velocity and changing vertical velocity. ___________________________________________________________________________ HORIZONTAL AND VERTICAL COMPONENTS Vertical component: - Influenced by gravity. - Relates to the maximum height achieved by the projectile. - Influenced by gravity. Horizontal component: - Not affected by a force (neglecting air resistance). - Related to the distance a projectile travels. - Influenced by air resistance. ___________________________________________________________________________ GRAVITY * Accelerates bodies in a vertical direction toward the surface of the earth. * Affects vertical component. * A constant, unchanging force that produces a constant downward acceleration (-9.81m/s/s). Projectile trajectories without gravitational influence Projectile trajectories with

F = G.m 1.m2/r2 influence gravitational (parabola)

Force = Universal constant (6.67 x 10-11). Masses of the 2 objects/ distance between 2 objects2 Apex: The highest point in the trajectory of a projectile. - The applied vertical velocity equals gravity. - Point where the object stops moving upward and starts moving downward. ___________________________________________________________________________ AIR RESISTANCE * Affects horizontal component of projectile velocity. E.g. A ball thrown in an outdoor area will travel much farther if it’s thrown with a tailwind rather than into a head wind. * Also affects the velocity of a projectile dropping vertically through the air. E.g. A sky diver’s velocity is much smaller after the opening of a parachute than before its opening. ___________________________________________________________________________ FACTORS INFLUENCING PROJECTILE TRAJECTORY Projection speed (v)

Projection angle (θ)

Projection height (h)

Range (R)

1. Projectile Speed: The magnitude of projectile velocity. - Speed of release. 2. Projectile Angle: The direction at which a body is projected with respect to the

Horizontal. - Angle of release. - Can be manipulated through throwing technique. - Optimum angle of projection: * Produces maximum horizontal displacement. * 45°. 3. Projection Height: The difference between projection height and landing height. - Height of release.

WEEK 7: LEVERS AND THE BODY AS A MACHINE:     

Machines and the body as a machine Lever systems and how they work The musculoskeletal system as a machine Lever types in the body and applied examples Mechanical advantage

LEVERS Lever: A simple machine consisting of a relatively rigid, bark-like body that may be made to rotate about an axis. * When muscles develop tension, pulling on bones to support or move the resistance created by the weight of the body segment(s), the muscle and bone are functioning mechanically as a lever. *Purpose is to transmit energy from one place to another. Fulcrum: The point of support, or axis about which a lever may be made to rotate. 1st Class Lever: Stability * Applied force and resistance are located on opposite sides of the fulcrum. * Very rare. E.g. Elbow extension against resistance, as in a tricep extension.

______________________________ Class lever: Strength (force) * Applied force and resistance are on the same side of the axis, with resistance closer to the axis. * More 2nd class levers than first class. E.g. Calf (gastrocsoleus) muscles working to elevate the body onto its toes. 2nd

3rd Class lever: Speed

* Applied force and resistance on the same side of the axis, with the applied force closer to the axis. * Most common lever in the human body. E.g. The forearm.

________________________________________ Mechanical Advantage: The mechanical effectiveness of a lever for moving a resistance. * The ratio of the moment arm of the force to the moment arm of the resistance. Mechanical advantage =

Moment arm (force) Moment arm (resistance)

* As fulcrum placement changes, the relative lengths of the moment arms for the motive and resistive forces varies. * Fulcrum in middle: - Moment arms are the same length. - No advantage. * Fulcrum further away from motive force: - Moment arm becomes longer. - Mechanical advantage (number greater than one). * Fulcrum closer to motive force: - Moment arm for resistive force becomes longer. - Resistive force has the advantage. E.g. A Wheelbarrow ____________________________________________________________ _______________ ANATOMICAL LEVERS * Skilled athletes maximize the length of the effective moment arm for force application, in order to maximize the effect of the torque produced by muscles about a joint.

E.g. Tennis serve. - Players hit the ball with the arm fully extended, as well as vigorously rotating the body in the transverse plane, making the spine the axis of rotation and maximizing the length of the anatomical lever delivering the force. - The longer the radius of rotation, the greater the linear velocity of the racquet head, and the greater the velocity of the struck ball. * Most levers in the body are 3rd class, so they have a mechanical advantage of less than one. * The angle at which the muscle pulls on the bone also affects the mechanical effectiveness of the muscle-bone lever system. * As joint angle and mechanical advantage change, muscle length also changes. ___________________________________________________________________________

ANGULAR KINEMATICS:     

Why angular and what is this movement? Angular equivalents of linear quantities. Relative and absolute angles. Angular displacement, velocity and acceleration. Moment of inertia.

Relative Angle: The angle formed between the longitudinal axes of adjacent body segments. E.g. The relative angle of the knee is formed by the longitudinal axis of the thigh and the lower leg. Absolute Angle: Angular orientation of a body segment with respect to a fixed line of reference. * Orientations of the body segments themselves (such as when the trunk is in flexion). ___________________________________________________________________________ ANGULAR DISTANCE AND DISPLACEMENT Angular displacement: The change in the angular position or orientation of a line segment. - Counter clockwise direction= Positive (+) - Clockwise direction= Negative (-)

Angular distance: The sum of all angular changes undergone by a rotating body. E.g. If the angle at the elbow joint changes from 90° to 160° during the flexion phase of a forearm curl exercise, the angular distance covered is 70°. Radian: Unit of angular measure used in angular-linear kinematic quantity conversions; equal to 57.3°. _____________________________________________________________________

ANGULAR SPEED AND VELOCITY Angular speed = Angular distance Change in time σ=φ Δt Angular velocity: The change in angular position, or the angular displacement, that occurs during a given period of time. Angular velocity = change in angular position Change in time

Angular velocity = Angular displacement Change in time OR

ω = Δ angular position Δ time

ω=θ Δt

ω = angular position2 – angular position1 time2 – time1 * Measured in: - degrees per second (deg/s). - radian per second (rad/s). - revolutions per second (rev/s). - revolutions per minute (rpm). ___________________________________________________________________________ ANGULAR ACCELERATION Angular acceleration: Rate of change in angular velocity. Angular acceleration = Change in angular velocity Change in time

α = Δω Δt α = ω2 – ω1 t2 - t1 ___________________________________________________________________________ MOMENT OF INERTIA Inertia: A body’s tendency to resist acceleration. * According to Newton’s 2nd law, the greater a body’s mass, the greater its resistance to linear acceleration. Therefore mass is a body’s inertial characteristic for considerations relative to linear motion. Moment of Inertia: Inertial property for rotating bodies representing resistance to angular acceleration. - Based on both mass and the distance the mass is distributed from the axis of rotation. I = mr2 * The distribution of mass with respect to the axis of rotation is more important than the total amount of body mass in determining resistance to angular acceleration, because r is squared. * Since r is the distance between a given particle and an axis of rotation, values of r change as the axis of rotation changes. Therefore when a player grips a baseball bat, ‘choking up’ on the bat reduces its moment of inertia with respect to the axis of rotation and the player’s wrists. The first baseball bat is harder to swing than the second, because the weight ring on it is positioned further from the axis of rotation.

* During sprinting, extreme flexion at the knee reduces the moment of inertia of the swinging leg. ___________________________________________________________________________

DETERMINING MOMENT OF INERTIA I = mk2

Moment of inertia = body mass x radius gyration2 Radius gyration: The object’s mass distribution with respect to a given axis of rotation. It is the distance from the axis of rotation to a point at which the mass of the body can theoretically be concentrated without altering the intertial characteristics of the rotating body. ___________________________________________________________________________ HUMAN BODY MOMENT OF INERTIA * The axis of rotation for a body segment in sagittal and frontal plane motions is typically an axis passing through the centre of a body segment’s proximal joint. * When a segment rotates around its own longitudinal axis, its moment of inertia is quite different from its moment of inertia during flexion and extension, or abduction and adduction, because its mass distribution, and therefore moment of inertia, is markedly different with respect to this axis of rotation. Principle axis: Three mutually perpendicular axes passing through the total bosy center of gravity. - The transverse (or frontal). - The anteroposterior (or sagittal). - The longitudinal (or vertical). Principle moment of inertia: Total- body moment of inertia relative to one of the principle axes.

WEEK 8/9: ANGULAR KINETICS SEGMENT SEQUENCING:       

Angular equivalents of Newton’s laws. Conservation of angular momentum. Angular impulse. Centripetal and centrifugal force. Linear and angular velocity. Characteristics of implements. Kinetic chains.

ANGULAR MOMENTUM Linear Momentum: The product of the linear inertial property (mass) and linear velocity. Angular Velocity: * Quantity of angular motion possessed by a body. * Measured as the product of moment of inertia and angular velocity. For linear motion: M = mv For angular motion: H = Iω Or: H = mk2 ω Three factors that affect the magnitude of a body’s angular momentum: * Mass (m): - No angular velocity = no angular momentum. - Increased mass = Increased angular momentum. * Distribution of that mass with respect to the axis of rotation (k): - Most dramatically influences angular momentum. * The angular velocity of the body (ω): - Increased angular velocity = Increased angular momentum. ___________________________________________________________________________ CONSERVATION OF ANGULAR MOMENTUM * Angular momentum is conserved whenever gravity is the only acting external force.

* Conserving angular momentum is useful in diving, trampolining and gymnastics- events where the body undergoes controlled rotations while airborne. E.g. Diving: - Diver leaves springboard with a fixed amount of angular momentum. - The amount of angular momentum present at the instant takeoff remains constant throughout the dive. - As the diver goes from an extended layout position into a tuck, the radius of gyration is decreased, thus reducing the body’s principal moment of inertia about the transverse axis. - Due to the constant angular momentum, an increase in angular velocity must accompany the decrease in moment of inertia. - The tighter the diver’s tuck, the greater the angular velocity. - Once the somersault is completed, the diver extends to a full layout position, increasing total-body moment of inertia with respect to the axis of rotation. TRANSFER OF ANGULAR MOMENTUM * Transferring angular velocity at least partially from one principal axis of rotation to another is possible. E.g. When a diver changes from a primarily somersaulting rotation to one that is primarily twisting, and vice versa. * This manipulation uses at least two body segments. * It is easier to initiate rotation about the longitudinal axis than the transverse or the anteroposterior principal axes. ___________________________________________________________________________ ANGULAR ANALOGUES (ANGULAR VERSIONS) OF NEWTON’S LAWS OF MOTION Newton’s 1st Law: - A rotating body will maintain a state of constant rotational motion unless acted on by an external torque. Newton’s 2nd Law: T = Iα - A net torque produces angular acceleration of a body that is directly proportional to the magnitude of the torque, in the same direction as the torque , and inversely proportional to the body’s moment of inertia. Newton’s 3rd Law:

- For every torque exerted by one body on another, there is an equal and opposite torque exerted by the second body on the first. ________________________________________________________...