Chapter 3 Biomechanics Concepts I Biomechanics: Study of biological systems by means of mechanical principles Sir Isaac Newton, father of Mechanics

Basic types of Motion Linear Angular or rotational Combined or general rectilinear curvilinear Angular or rotational Combined or general

Human Analysis Internal: mechanical factors creating and controlling movement inside the body External: factors affecting motion from outside the body

Kinematics Describes motion Vectors Angular and linear quantities Time Position Displacement Velocity Acceleration Vectors Angular and linear quantities

Kinematics Formulas

Kinetics Explains causes of motion Axis Mass amount of matter (kg) Inertia: resistance to being moved Moment of Inertia (rotation) I = m·r2 Axis

Kinetics Force: push or pull that tends to produce acceleration Important factor in injuries Vector

Kinetics Idealized force vector Force couple system d F F’ F M=Fd d d

Kinetics: Force Force & Injury factors Magnitude Location Direction Duration Frequency Variability Rate

Kinetics: Force System Linear Parallel Concurrent General Force Couple

Center of Mass or Gravity Imaginary point where all the mass of the body or system is concentrated Point where the body’s mass is equally distributed

Pressure P = F/A Units (Pa = N m2) In the human body also called stress Important predisposing factor for injuries

Moments of Force (Torque) Effect of a force that tends to cause rotation about an axis M = F ·d (Nm) If F and d are  Force through axis

Moments of Force (Torque) Force components Rotation Stabilizing or destabilizing component

Moments of Force (Torque) Net Joint Moment Sum of the moments acting about an axis Human: represent the muscular activity at a joint Concentric action Eccentric action Isometric

Moments of Force (Torque) Large moments tends to produce injuries on the musculo-skeletal system Structural deviation leads to different MA’s

1st Law of Motion A body a rest or in a uniform (linear or angular) motion will tend to remain at rest or in motion unless acted by an external force or torque Whiplash injuries

2nd Law of Motion A force or torque acting on a body will produce an acceleration proportional to the force or torque F = m ·a or T= I · F

3rd Law of Motion For every action there is an equal and opposite reaction (torque and/or force) Contact forces: GRF, other players etc. GRF

Equilibrium Sum of forces and the sum of moments must equal zero Dynamic Equilibrium Must follow equations of motions  F = m x a  T = I x 

Work & Power Mechanical Work Power: rate of work W= F ·d (Joules) W= F ·d·cos () Power: rate of work P = W/t (Watts) P = F ·v P = F ·(d/t) d W

Mechanical Energy Capacity or ability to do work Accounts for most severe injuries Classified into Kinetic (motion) Potential (position or deformation)

Kinetic Energy Body’s motion Linear or Angular KE=.5·m·v2 KE=.5 ·I·2

Potential Energy Gravitational: potential to perform work due to the height of the body Ep= m·g·h Strain: energy stored due to deformation Es= .5·k·x2

Total Mechanical Energy Body segment’s: rigid (nodeformable), no strain energy in the system TME = Sum of KE, KE, PE TME = (.5·m ·v2)+(.5 ·I ·2)+(m ·g ·h )

Momentum P Quantity of motion p=m ·v (linear) Conservation of Momentum Transfer of Momentum Injury may result when momentum transferred exceeds the tolerance of the tissue Impulse = Momentum

Angular Momentum Quantity of angular motion H=I · (angular) Conservation of angular momentum Transfer of angular momentum

Collisions Large impact forces due to short impact time Elastic deformation Plastic deformation (permanent change) Elasticity: ability to return to original shape Elastoplastic collisions Some permanent deformation Transfer and loss of energy & velocity Coefficient of restitution e=Rvpost/Rvpre

Friction Resistance between two bodies trying to slide Imperfection of the surfaces Microscopic irregularities - asperities Static friction f< s·N Kinetic f=µk·N f N

Friction Rolling: Lower that static and kinetic friction (100-1000 times) Joint Friction - minimized Blood vessels - atherosclerosis

Fluid mechanics Branch of mechanics dealing with the properties and behaviors of gases & fluids

Fluid Flow Laminar Turbulent Effects of friction on arterial blood flow

Fluid Forces Buoyancy Drag Lift Magnus forces Viscosity Surface Pressure Wave Lift Magnus forces Viscosity Biological tissue must have a fluid component

Fluid Forces