mechanics and materials forces displacement deformation (strain) translations and rotations stresses...
TRANSCRIPT
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Mechanics and Materials
Forces
Displacement
Deformation (Strain)
Translations and Rotations
Stresses
Material Properties
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Jamshidi AA, PT 2
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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Jamshidi AA, PT 3
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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Jamshidi AA, PT 4
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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Jamshidi AA, PT 5
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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Jamshidi AA, PT 6
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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Jamshidi AA, PT 7
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
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Jamshidi AA, PT 8
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
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Forces and
Equilibrium
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Newton's Laws
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Jamshidi AA, PT 11
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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Jamshidi AA, PT 12
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 ρ2
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Jamshidi AA, PT 13
Mass moment of inertia of a body
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Jamshidi AA, PT 14
Center of mass & Change of the Mass moment of inertia
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Jamshidi AA, PT 15
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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Jamshidi AA, PT 16
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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Jamshidi AA, PT 17
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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Jamshidi AA, PT 18
Impulse-momentum relationshipground reaction force as an individual ran
A>B: forward momenum is decreased
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Jamshidi AA, PT 19
• 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.)
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Jamshidi AA, PT 20
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
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Movement Analysis
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Jamshidi AA, PT 22
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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Jamshidi AA, PT 23
Free Body Diagram
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Jamshidi AA, PT 24
Basic Dynamics
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MomentsForces applied at a distance from the center of
rotation cause the body to rotate.
F
x
FxMwall
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Jamshidi AA, PT 26
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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Jamshidi AA, PT 27
Mechanical Advantage > or = or < 1
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Jamshidi AA, PT 28
Mechanical Adventage > 1
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Jamshidi AA, PT 29
Mechanical Adventage < 1
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Jamshidi AA, PT 30
Line of Force & Moment Arm
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Jamshidi AA, PT 31
Internal & External TorquesStatic Rotary Equilibrium
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IUMS Jamshidi PhD_PT 32
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Jamshidi AA, PT 33
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Jamshidi AA, PT 34
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Jamshidi AA, PT 35
Change in the Knee Angle
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Jamshidi AA, PT 36
Change in Moment Arm
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Jamshidi AA, PT 37
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Jamshidi AA, PT 38
USING A CANE
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Jamshidi AA, PT 39
Carrying Externa Load