Mechanics and Materials Forces Displacement Deformation (Strain) Translations and Rotations Stresses Material Properties

Jamshidi AA, PT2 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, PT3 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, PT4 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, PT5 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, PT6 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, PT7 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, PT8 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 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, PT12 Newton’s First Law LAW 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 ρ 2

Jamshidi AA, PT13 Mass moment of inertia of a body

Jamshidi AA, PT14 Center of mass & Change of the Mass moment of inertia

Jamshidi AA, PT 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, PT16 Newton’s Second Law LAW 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, PT17 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, PT18 Impulse-momentum relationship ground reaction force as an individual ran A>B: forward momenum is decreased

Jamshidi AA, PT19 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, PT20 Newton’s Third Law LAW 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, PT22 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, PT23 Free Body Diagram

Jamshidi AA, PT24 Basic Dynamics

Moments Forces applied at a distance from the center of rotation cause the body to rotate. F x

Jamshidi AA, PT26 Lever Systems Rigid rod fixed at point to which two forces are applied 1 st class 2 nd class 3 rd class Functions –  applied force –  effective speed RF R F FR

Jamshidi AA, PT27 Mechanical Advantage > or = or < 1

Jamshidi AA, PT28 Mechanical Adventage > 1

Jamshidi AA, PT29 Mechanical Adventage < 1

Jamshidi AA, PT30 Line of Force & Moment Arm

Jamshidi AA, PT31 Internal & External Torques Static Rotary Equilibrium

IUMSJamshidi PhD_PT32

Jamshidi AA, PT33

Jamshidi AA, PT34

Jamshidi AA, PT35 Change in the Knee Angle

Jamshidi AA, PT36 Change in Moment Arm

Jamshidi AA, PT37

Jamshidi AA, PT38 USING A CANE

Jamshidi AA, PT39 Carrying Externa Load