Principles of Biomechanical Analysis

PSE4U Mr. MacMillan

Review of Biomechanics

 The Laws of Motion  1 st – Law of Inertia   2 nd 3 rd – Law of Acceleration – Law of Reaction

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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

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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

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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 Motion

Linear Motion

Displacement Velocity Acceleration Force Mass

Rotational Motion

Angular Displacement Angular Velocity Angular Acceleration Moment of Force (torque) Moment of Inertia

Ice Skating

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

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

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)

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Seven Principles of Biomechanical Analysis

Stability Maximum force Maximum velocity Impulse Reaction Torque Angular momentum

Principle 1:

 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 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.

 Force = m a   M = mass A = acceleration     Acceleration  = (v – u) / t    V = final velocity U = starting velocity T = time Momentum = m v   M = mass V = velocity Impulse (N/s)  = Ft = m Δv  M = mass  Δ v = average velocity Change in Momentum  = m (V2 – v1)  M = mass   V2 = final velocity V1 = initial velocity

Biomechanical Formulae

Your Task!

  Read pages 230 – 234 Answer Questions on Handout on course website