Jamshidi AA, PT 1

1.1 Mechanics• Mechanics

– Branch of physics concerned with motion and deformation of bodies, which are acted upon by mechanical disturbances (forces)

– Oldest of all physical sciences• Engineering (or "Applied") mechanics

– Science of applying the principles of mechanics– Concerned with the analysis and design of

mechanical systems– Three main parts…

Jamshidi AA, PT 2

1.2 Biomechanics (cont.)• Biomechanics (cont.) -- why?

– Has led to improvements of understanding of many physiological processes

– Contributed to development of medical diagnostic and treatment procedures

– Provided means to design and manufacture medical devices, surgical tools, aids for the handicapped

– Suggested means for improving human performance in workplace and in athletics

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1.2 Biomechanics (cont.)

• Components of applied mechanics in biomechanics– Determine magnitude, nature of forces at joints

and in muscles (statics)– Motion analysis, sports mechanics (dynamics)– Development of basic equations of biological

materials and systems (mechanics of materials)– Investigation of blood flow in circulation, air flow

in lungs (fluid mechanics)

Mechanics and Materials

Forces

Displacement

Deformation (Strain)

Translations and Rotations

Stresses

Material Properties

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Stress

• Stress (): internal resistance to an external load– Axial (compressive or tensile)

=F/A– Shear = F/A (parallel or

tangential forces)

• Units Pascal (Pa) = 1Nm2

Axial

Shear

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Strain• Change in shape or deformation ()• Absolute strain• Relative strain

– L/Lo

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Musculoskeletal forcesthe same forces that move and stabilize the body also have the potential to

deform and injure the body

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A stress-strain curve for tendonFive distinct regions

A.toe regionB. linear

regionC. progressive

failure region

D.major failure region

E. complete rupture region

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• Toe region: there is little increase in load with lengthening

• Linear region: increased elongation requires disproprtionately larger amounts of stress. Microfailure of the tendon begins early in this region (2 to 6% strain).

• Region of progressive failure: the slope of the stress-strain curve begins to decrease, indicating microscopic disruption. The gross tissue appears to be normal and intact (6% strain).

• Region of major failure: The slope of the stress-strain curve now flattens dramatically. There is visible narrowing at numerous points of shear and rupture (6 to 12% strain).

• Region of complete rupture: The slope of the stress-strain curve falls off, indicating a total break in the gross tendon. (12 to 15% strain)

Mechanics and Materials

Forces

Displacement

Deformation (Strain)

Translations and Rotations

Stresses

Material Properties

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1.3 Basic Concepts

• Newtonian mechanics are based on:– Length (L; quantitative measure of size)– Time (T; concept for ordering flow of events)– Mass (M; quantitative measure of inertia, the

resistance to change in motion, of matter)

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1.3 Basic Concepts

• Derived concepts:– Velocity (time rate of change of position)– Acceleration (time rate of increase of velocity)– Force (action of one body on another, or a

mechanical disturbance or load)– Moment/Torque (quantitative measure of twisting

action of a force on a body)

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Kinematics• Description of the movement of the body,

independent of the forces or torque that cause movement and include:

• Linear & Angular displacement• Velocities• Accelerations

– Type of motion• Translation: linear motion in which all part of a rigid body move

parallel to and in the same direction as every other parts. • Rotation: all points in the rigid body simultaneously moves in a

circular path about some pivot point (axis of rotation).

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Kinetics• Describe the effect of forces on the body.

– Force: push or pull that can produce, arrest or modify movement.

– Newton’s second law: quantity of a force (F) can be measured by product of the mass (m) multiplied by the acceleration (a) of the mass. Force is zero when the acceleration is zero.

• Kinetic analysis include: moment of force produced by muscles crossing a joint, the mechanical power flowing from muscles, energy changes of the body

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Musculoskletal forces• Internal Forces: produced from structures located

within the body.– Active force (stimulated muscle)– Passive force (ligament, capsule or intramuscular connective

tissue, friction)• External Forces: produced by forces acting from

outside the body.– Gravity– Ground– External load– Physical contact

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Vector: a quantity that is completely specified by its magnitude and direction

Factors required to describe a vector

• Magnitude: length of the arrow

• Direction: spatial orientation of the shaft of the arrow

• Sense: orientation of the arrowhead

• Point of application: where the base of arrow contact the body

Jamshidi AA, PT 17

Vector: a quantity that is completely specified by its magnitude and direction.

Factors required to describe a vector

• Magnitude: length of the arrow

• Direction: spatial orientation of the shaft of the arrow

• Sense: orientation of the arrowhead

• Point of application: where the base of arrow contact the body

Forces and

Equilibrium

Newton's Laws

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1.4 Newton's Laws

• Newton's first law:– A body at rest will remain at rest; a body

in motion will remain in motion – Bodies in motion will travel at constant

velocity and in a straight line– Requires the sum of the forces acting on

a body to be zero (thus, the body is in equilibrium)

– SF = 0 – SM = 0

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Newton’s First LawLAW OF INERTIA

• Inertia is related to the amount of energy required to alter the velocity of a body

• The inertia within a body is directly proportional to its mass• Center of mass is where the acceleration of gravity acts on

the body (center of gravity)• Mass moment of inertia of a body is a quantity that

indicates its resistance to a change in angular velocity

• I = m X r2

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Mass moment of inertia of a body

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Center of mass & Change of the Mass moment of inertia

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1.4 Newton's Laws (cont.)

• Newton's second:– A body with a nonzero net force will

accelerate in the direction of the force– The magnitude of the acceleration is

proportional to the magnitude of the force

– SF = m * a– Thus, the first law is a special case of

the second law

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Newton’s Second LawLAW OF ACCELERATION

• Linear motion: force-acceleration relationship• ΣF = m X a

– ΣF designate the sum of or net forces

• Rotary motion: torque-angular acceleration relationship• ΣT = I X α

– ΣT designate the sum of or net forces

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Impulse-momentum relationship

• F = m X v/t Ft = m X v• Linear momentum = mass X linear velocity• Linear impulse = force X time

• T = I X ω/t Tt = I X ω• Angular momentum = I X angular velocity• Angular impulse = torque X time

• Momentum: quantity of motion possessed by a body• Impulse: what is required to change the momentum

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Impulse-momentum relationshipground reaction force as an individual ran

A>B: forward momenum is decreased

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• Newton's third law:– For every action, there is an equal and

opposite reaction ("if you push against the wall, it will push you back")

– The forces of action and reaction are equal in magnitude but in the opposite direction

– Important for helping draw free body diagrams, and concept of "normal" force

1.4 Newton's Laws (cont.)

Jamshidi AA, PT 29

Newton’s Third LawLAW OF ACTION-REACTION

• Every effect one body exerts on another is counteracted by an effect that the second body exerts on the first

• The two body intact is specified by the law of acceleration ΣF = m X a

• Each body experiences a different effect and that effect depends on its mass

Movement Analysis

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Movement Analysis• Anthropometry: measurement of physical design of human

body (length, mass…) • Free body diagram: simplified sketch that presents the

interaction between a system and its environment

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Free Body Diagram

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Basic Dynamics

MomentsForces applied at a distance from the center of

rotation cause the body to rotate.

F

x

FxMwall

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Lever Systems

• Rigid rod fixed at point to which two forces are applied

• 1st class • 2nd class• 3rd class• Functions

– applied force– effective speed

R F

RF

FR

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Mechanical Advantage > or = or < 1

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Mechanical Adventage > 1

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Mechanical Adventage < 1

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Line of Force & Moment Arm

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Internal & External TorquesStatic Rotary Equilibrium

IUMS Jamshidi PhD_PT 41

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Change in the Knee Angle

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Change in Moment Arm

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USING A CANE

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Carrying Externa Load