Basic Concepts of BioMechanics

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Basic Concepts of (Bio)Mechanics

• D. Gordon E. Robertson, Ph.D.
• Biomechanics Laboratory,
• School of Human Kinetics,
• University of Ottawa, Ottawa, CANADA

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Mathematics

• pi (p) ratio of circumference to diameter
• commutative rule ab ba
• associative rule abccabetc.
• distributive rule r(ab) ra rb
• order of operations ( ), xn, / , -
• zero 0 x 0 , 0 x x
• vector algebra a b b a etc.

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Trigonometry

• Polar to Rectangular components
• x r cos q
• y r sin q
• Rectangular to Polar components
• r2 x2 y2
• q tan-1 (y/x)
• Moment of force
• M r F sin q
• Work of a force
• W F s cos q

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Fundamental Quantities

• Seven base units plus radian (angle) and
  steradian (solid angle)
• space the metre (m)
• mass the kilogram (kg)
• time the second (s)
• amount of a substance the mole (mol)
• light intensity the candela (Ca)
• temperature the kelvin (K)
• electrical current (flow) the ampere (A)

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Fundamental LawsFirst Law (Statics)

• F 0 therefore linear momentum is constant
• (I.e., velocity v constant)
• If linear velocity is constant the body is
  traveling in a straight line at constant speed
• F is called the Resultant Force and is equal to
  the sum of ALL forces acting on the body
• M 0 therefore angular momentum is constant but
  rate of spin can be changed by altering the
  bodys moment of inertia

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Fundamental LawsSecond Law (Dynamics)

• S F m a
• therefore linear velocity is changing and/or body
  is traveling along a curved path
• this is called acceleration
• direction of acceleration is same as direction of
  resultant force
• M I a therefore angular momentum changes

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Fundamental Laws Third Law (Reaction)

• Every force (F) requires a reaction force (Z).
• The reaction force is equal in magnitude but
  opposite in direction.
• F Z 0 where Z -F
• I.e., F cannot exist without Z

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Fundamental LawsUniversal Law of Gravitation

• Gravity
• every mass particle in the universe experiences a
  force of attraction from every other particle
• most of these forces are so small they can be
  ignored
• exception is the Earth because of its large mass
  and nearness, which exerts a force called weight
• weight W G(m mearth) / r2
• G Universal gravitational constant
• m mass of a body
• mEarth mass of Earth
• r distance from body to centre of Earth

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Fundamental LawsWeight vs. Mass

• Weight
• gravitational force exerted by large masses
  (Earth, Moon, Jupiter) on bodies near their
  surfaces
• Given g 9.81 m/s2 G(mEarth) / r2
• weight m g
• Thus, 1 kilogram 9.81 newtons
• to change from weight in newtons to mass
• divide by 9.81 (mass W/g)
• to convert from mass in kilograms to weight
• multiply by 9.81 (weight m g)

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Laws or PrinciplesDerived from Experiment

• Dry Static Friction
• Coeff. of static friction ms (Fs/N)
• Fs maximum force before slippage occurs
• N normal force (force perpendicular to surface)
• Dry Kinetic Friction
• Coeff. of kinetic friction mk (Fk/N)
• Fs frictional force during motion
• Hookes Law (for Linear Springs)
• Spring constant k -Fspring /(L-L0)
• L-L0 change in length (deformation from rest
  L0)

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Derived Laws and Principles

• Conservation of Linear Momentum
• when resultant force is zero linear momentum is
  constant
• Conservation of Angular Momentum
• when resultant moment is zero angular momentum is
  constant
• Conservation of Mechanical Energy
• mechanical energy is constant when resultant
  force is a conservative force or the sum of
  conservative forces
• Work Energy Principle
• Work change in mechanical energy
• Impulse Momentum Principle
• Impulse change in momentum