Principles of Biomechanical AnalysisPSE4U

Review of Biomechanics The Laws of Motion

1st – Law of Inertia 2nd – Law of Acceleration 3rd – Law of Reaction

Types of Motion Linear

Movement in a particular direction Sprinter accelerating down a track

Rotational Movement about an axis What are the three axis’?

Longitudinal, anterio-posterior, horizontal Ice skater spinning or a gymnastic

somersault

Linear Motion Acceleration in a straight line Force as a vector

Force as a pull or push of a certain magnitude in a certain direction

Rotational Motion Is comparable to linear motion but the

object spins around an axis Acceleration is angular Torque is measured rather than force Moment of inertia

Resistance to rotation Larger the moment of inertia, the

larger the moment of force needed to maintain the same angular acceleration

Linear and Rotational MotionLinear Motion Rotational Motion

Displacement Angular Displacement

Velocity Angular Velocity

Acceleration Angular Acceleration

Force Moment of Force (torque)

Mass Moment of Inertia

Ice Skating

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The ice-skater begins to spin with arms spread apart then suddenly brings them closer to the body. The end result of tightening up is that the skater’s spin (angular velocity) increases, seemingly miraculously

Gymnastics

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Following a series of rapid somersaults in a tight position, the gymnast does a forward flip with the body positioned more or less straight. By opening up, the gymnast increases the moment of inertia, thereby resulting in a decrease in angular velocity

Diving

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After leaving the high diving board, the diver curls tightly and then opens up just before entering the water. By opening up before entry, the diver increases the moment of inertia, thereby slowing down the angular velocity and hopefully ensuring a smooth and safe entry.

The Lever Systems Class I Lever Class II Lever Class III Lever

The fulcrum (axis) is located between the force (effort) and the resistance (load)

Class I Lever (e.g. teeter-totter)

The resistance is between the fulcrum and the resistance

Class II Lever(e.g. wheelbarrow)

The force is between the fulcrum and the resistance

Class III Lever

(e.g. snow shovel)

Seven Principles of Biomechanical Analysis

1. Stability2. Maximum force3. Maximum velocity4. Impulse5. Reaction6. Torque7. Angular momentum

The lower the centre of mass, the larger the base of support, the closer the centre of mass to the base of support, and the greater the mass, the more stability increases.

Principle 1 – Stability

Stability is also Affected By: Collisions The Surface

Friction Angle

Inner Ear Sight Readiness

Increasing Stability1. Lower the C of G2. Increase the mass3. Increase the size of the base of support

- The further the center of gravity (use the line dropped from it) is from the edge of the base of support, the more stable the athlete is

Applications of Stability What are points in sports you play that

you use maximum force?

What are points in your day to day life that you use maximum force?

Are there times when it is ok to be unstable?

Principle 2: The production of maximum force

requires the use of all possible joint movements that contribute to the task’s objective

Principle 3: The production of maximum velocity

requires the use of joints in order – from largest to smallest

Principle 4: The greater the applied impulse, the

greater the increase in velocity

Principle 5: Movement usually occurs in the

direction opposite that of the applied force

Principle 6: Angular motion is produced by

application of force acting at some distance from an axis, that is, by torque

Principle 7: Angular momentum is constant when an

athlete or object is free in the air.

Free Body Diagrams Free body diagrams, are a tool for solving problems with

multiple forces acting on a single body. The purpose of a free body diagram is to reduce the

complexity of situation for easy analysis. The diagram is used as a starting point to develop a mathematical model of the forces acting on an object.

Below is a picture of a flying jet.

Equilibrium, Balance, & Stability

Equilibrium is the state of zero acceleration (static or dynamic)

Balance is the ability to control equilibrium

Stability is a resistance to the disturbance of equilibrium

Factors Influencing Balance1. Location of the center of gravity in

relation to the base of support2. Size of the base of support3. Mass of the person4. Height of the center of gravity5. Traction/friction6. Sensory perceptions

Biomechanical FormulaeForce

Force = m a – the force acting on an object F=ma The BULL RUSH

M = mass A = acceleration

Race Car Example

Biomechanical FormulaeAcceleration

Acceleration = Change in Velocity ÷ Time a = (v2-v1) ÷ t where a = acceleration

v2 = final velocity (the one it ended up with) v1 (u) = initial velocity (the one it started with)

t = time

This equation can be rearranged.

Example 1. If a car changes from 10 m/s to 30 m/s in 8 seconds, what is its acceleration? v2 = 30 m/s

v1 = 10 m/st = 8 s

a = (30 - 10) ÷ 8 = 20 ÷ 8 = 2·5 m/s2

Acceleration ExampleExample 2. If a bicycle moving at 15 m/s takes 10 seconds to stop,

what is its acceleration? In this example, the final velocity is zero because

the bicycle has stopped. v2 = 0 m/s

v1 = 15 m/st = 10 s

a = (0 - 15) ÷ 10   = -15 ÷ 10   = -1·5 m/s2

The acceleration is negative because the bicycle has slowed down.

Biomechanical FormulaeMomentum

Momentum – product of the objects mass and it’s velocity (rate of speed)

P = m v M = mass V = velocity

A basketball ball having 2kg mass and 6m/s velocity moves to the east. What is it’s momentum?

Momentum Example A child having mass 25kg and velocity

2m/s moves to the west. What is his momentum?

Biomechanical FormulaeImpulse

Impulse (N/s) – product of a force applied over a time interval I = F(tf-ti)

tf = final time ti = initial time

What is the impulse imparted by a rocket that exerts 4.8 N for 1.63 seconds? I = ? F=4.8N tf= 1.63s ti = 0s

I = 4.8 * 1.63 = 7.824 or 7.8 Ns

Impulse Example What force exerted over 6 seconds gives

you an impulse of 64 Ns? I = 64Ns F= ? tf= 6s ti = 0s

64 = F (6-0) = 64/6 =10.7 N

Biomechanical FormulaeImpulse - Momentum

Impulse-Momentum Relationship – in order for an object to experience a change in momentum, an impulse must be applied

F(tf-ti) = m(v2 – v1)

F = Force (N) tf = final time ti = initial time M = mass V2 = final velocity V1 = initial velocity

Impulse-Momentum ExampleHitting a pitched baseball. A baseball of mass 0.14 kg is pitched at a batter with an initial velocity of -38 m/s (negative is towards the bat). The bat applies an average force that is much greater than the weight of the ball, and the ball departs from the bat with a final velocity of +58 m/s. Assuming that the time of contact with the bat is 1.6 x 10-3 s, find the average force exerted on the ball by the bat.

F(tf-ti) = m(v2 – v1) F = ? tf = 0.0016s ti = 0 s M = 0.14kg V2 = 58 m/s V1 = -38 m/s

F(tf-ti) = (0.14)(58) - (0.14)(-38) F(0.0016) = +13.44kg m/s F = (13.44)/(0.0016) = +8400 N

Applications in Biomechanics Performance improvement

Coaches and athletes focused on “performance improvement” within the aspects of technique and sport training

Injury prevention and rehabilitation High level of interest in biomechanics from sports

medicine specialists, trainers, and injured athletes in relation to “injury prevention and rehabilitation”

Fitness and personal training Biomechanical analysis can be applied both to exercise

and to equipment

Injury Prevention and Rehabilitation Progressive resistance training to improve muscular

endurance, size, and tensile strength of both muscle and connective tissue can be integrated into the off- and pre-season schedule

Specific design of aerobic and muscular warm-up tailored to the activities planned for the workout will bring more injury prevention value to the session

All key muscles to be used must be stretched Muscle imbalance needs to be addressed

Fitness and Personal Training Biomechanical analysis begins by examining the method

of execution of an exercise; such analyses enable one to give advice concerning: The position of joints to isolate specific muscles How to align the movement to the muscle How to combine muscles for optimal results The optimal speed for the objective The best starting position and range of motion for an

exercise How to modify the leverage to gain a greater strength

output

Your Task! Read pages 230 – 234