Analyzing Mechanical Systems


Analyzing Mechanical Systems
Topic 1: Simple Machines and Complex Systems
Part 1: Simple Machines
Inclined Plane

  • Also known as a Ramp
  • An angled surface
  • Used to help move a load up or down

    • Wedge
  • Two inclined planes joined back to back
  • Used to seperate objects or hold an object in place

    • Screw
  • A cylindrical wedge with an inclined plane wrapped around it
  • Used to move objects
  • Also used to fasten materials together

    • Pulley
  • A wheel and axle that supports a rope
  • Used to help move loads vertically or change the direction of force

    • Class One lever
  • The fulcrum sits in the middle of the force and load
  • Used for changing the direction of a force

    • Class Two lever
  • The load sits in the middle of the force and the fulcrum
  • Used for lifting heavy loads or generating a lot of force

    • Class Three Lever
  • The effort force is applied in the middle of the load and the fulcrum
  • Used for moving loads fast, far, and precise.

    • Wheel and Axle
  • A large wheel attatched on the top of a smaller cylinder
  • The rotation of one is transferred to the other
  • Wheels reduce friction
  • Wheels provide leverage by multiplying the amount of force that you put in.

    • Part 2: Compound Machines
    Compound machines: Devices made up of more than one simple machine. Like; Scissors, wheelbarrow, and lawnmowers.
    This depicts a Class 1 Lever with a wedge.
    Part 3: Gears
    What is a Gear? A gear is a wheel with teeth that meshes with another gear.

    Gears are used to change the speed, torque, and direction.

    Spur Gears

    Gears have an input (Driver) gear and an output (Driven) gear.

    A larger input gear gives you:
  • A speed advantage (faster)
  • Less torque
  • Increased speed

    • A smaller input gives you:
  • Less speed
  • More torque (Force Advantage)
  • Reduced speed

    • Speed Ratios

    The relationship between the speed of a smaller and a larger gear is called a speed ratio. It is calculated by dividing the number of input gear teeth by the number of output gear teeth.

    Speed ratio = Input teeth / Output Teeth

    Part 4: Pulleys
    What is a pulley?
  • A pulley uses a rope that goes around the wheel.
  • The rope usually has a force applied.

    • Fixed Pulley
  • Object moves
  • Pulley stays in the same spot
  • Force applied to only one end of a rope
  • Most basic form

    • Moveable Pulley
  • Pulley is attatched to object
  • Pulley and Object move together
  • Rope is attatched to something that does not move
  • Force is applied to the other end of the rope

    • Why use pulleys?
  • Pulleys redirect force
  • It's easier to move up to lift an object

    • Mechanical Advantage: More distance travelled, but with less force.

    Part 5: Complex Systems
    Components -> Subsystem -> System -> Complex Machine

    Topic 2: Analyzing Mechanical Systems
    Mechanical Advantage
    Machines make our work easier, Mechanical Advantage is a measurement of how a machine multiplies the force that was originally put in.

    Mechanical Advantage (MA) = Output force / Input force, force is measured in Newtons (N)!

    If the Mechanical Advantage is greater than 1, output force is greater. (Get's more force than you put in) MECHANICAL ADVANTAGE! Increases force.

    If the Mechanical Advantage is equal to 1, no change in amount of force. NO MECHANICAL ADVANTAGE! Changes direction of motion.

    If the Mechanical Advantage is less than 1, less force. NO MECHANICAL ADVANTAGE! Increases the speed.

    MA Formulas
    (For Levers) MA = Input arm Length (Effort) / Output arm Length (Load)

    Example A (Levers):
    Input = 150
    Output = 50
    MA = 150/50. MA = 3


    (For Ramps) MA = Ramp Length / Ramp Height

    Example B (Ramps): Length = 10m
    Height = 1m
    MA = 10/1. MA = 10

    Determining Mechanical Advantage of Pulleys
    How can you find the Mechanical Advantage of a Pulley?
  • The Mechanical Advantage of a Pulley system is equal to the number of ropes supporting the movable load. Don't count the ropes only used for pulling.

    • Work
    When you exert force on an object and move the object some distance, you do work on that object.

    Work (W) = Force (F) x Distance (D)
  • Work is measured in Joules (J)
  • Force is measured in Newtons (N)
  • Distance is measured in meters (m) or converted

    • Pressure
    Hydraulic System
  • A system that uses a liquid under pressure to move loads

    • Pneumatic System
  • A system that uses gas under pressure to move loads.

    • Pressure (P) = Force (F) / Area (A)
  • Pressure is measured in Pascals (Pa)
  • Area is measured in squared meters (m²)

    • Piston: A disk that fits tightly inside a cylinder, Pistons create pressure.
  • As the disk moves, it either draws in fluids/gases, or pushes fluids/gases out
  • Commonly used in engines and hydraulic systems

    • A Hydraulic System uses a liquid under pressure to move loads, it uses a piston.
  • Input Piston is used to apply force to the fluid (Usually smaller)
  • Output Piston transfers the force to the load (Usually bigger)

    • Pascal's Law says Pressure is transmitted equal in all parts, the pressure of the input and the output piston is the same.

    Fi / Ai = Fo / Ao

    Pascal's Law
    Pressure applied to an enclosed fluid is transmitted equally in all directions.
  • Fluids cannot be compressed like gases
  • Pressure is transmitted equally (IMPORTANT POINT)

    • Part 6: Energy Sources
    A complex or mechanical system requires energy to perform tasks.

    Chemical Energy: Energy stored in food or a fuel (Anything using a battery)

    Mechanical Energy: Energy of objects in motion

    Electrical Energy: Any particles moving through a wire

    Thermal/Kinetic Energy: Energy of moving particles (heat)

    Elastic Energy: Energy from stretching