Mechanics and Materials

Forces

Displacement

Deformation (Strain)

Translations and Rotations

Stresses

Material Properties

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)

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)

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).

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

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

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

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

Forces and

Equilibrium

Newton's Laws

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

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

Jamshidi AA, PT 13

Mass moment of inertia of a body

Jamshidi AA, PT 14

Center of mass & Change of the Mass moment of inertia

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

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

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

Jamshidi AA, PT 18

Impulse-momentum relationshipground reaction force as an individual ran

A>B: forward momenum is decreased

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.)

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

Movement Analysis

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

Jamshidi AA, PT 23

Free Body Diagram

Jamshidi AA, PT 24

Basic Dynamics

MomentsForces applied at a distance from the center of

rotation cause the body to rotate.

F

x

FxMwall

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

Jamshidi AA, PT 27

Mechanical Advantage > or = or < 1

Jamshidi AA, PT 28

Mechanical Adventage > 1

Jamshidi AA, PT 29

Mechanical Adventage < 1

Jamshidi AA, PT 30

Line of Force & Moment Arm

Jamshidi AA, PT 31

Internal & External TorquesStatic Rotary Equilibrium

IUMS Jamshidi PhD_PT 32

Jamshidi AA, PT 33

Jamshidi AA, PT 34

Jamshidi AA, PT 35

Change in the Knee Angle

Jamshidi AA, PT 36

Change in Moment Arm

Jamshidi AA, PT 37

Jamshidi AA, PT 38

USING A CANE

Jamshidi AA, PT 39

Carrying Externa Load