Introduction to Simple and Complex Machines

Machines

Definition

A machine is a set of parts or organs coupled together, allowing direct or regulated action of a force with the goal of performing a job.

Components

A machine is formed by the structure and mechanisms. The mechanisms are coupled to each piece.

  • Structure: The bench, supports, feet, frame, etc.
  • Mechanisms: The axles, wheels, guides, pulleys, gears, crank, etc.

Types of Movement

The types of movement that a machine makes are:

  • Straight: The move follows a straight-line trajectory, both vertically and horizontally.
  • Curvilinear: The movement follows a curved trajectory.
  • Alternative: Moving in the same direction in alternating horizontal and vertical directions.

Physical Machines

Force: F = m * a [N = kg * m/s2] N = Newton
Work: W = F * x [J = N * m] J = Joule
Mechanical Power: P = W / t [CV = J / s] HP = Horsepower
Performance: ? = Wu / Wm [%]

Simple Machines

Simple machines use muscle power and serve as the basis for the design of other machines.

The basic simple machines are the lever, the inclined plane, wheel, screw, and crank.

Complex Machines

Complex machines are classified according to their purpose:

  • Motor Machines: Convert mechanical energy into other forms of energy, such as hydraulic, electrical, etc.
  • Generating Machines: (dynamos and alternators) Use hydropower, wind, fossil fuels, etc., and transform it into electricity.
  • Operational Machines: (jackhammer, climbing, etc.) Transform one type of energy (electricity, fossil fuels, etc.) into an alternative or rotary movement (mechanical work).

Lever

A lever is a rigid bar that rotates on a support called a fulcrum. It allows applying force to overcome resistance.

The closer the fulcrum is to the resistance, the less force is required to overcome it.

Types of Levers

  • First-class levers: The fulcrum is located between the power and the resistance. Examples: scales, pliers, scissors, swing, barrier level crossing.
  • Second-class levers: The resistance is between the power and the fulcrum. Examples: wheelbarrow, nutcracker, brake pedals in cars.
  • Third-class levers: The power is located between the fulcrum and the resistance. Examples: tongs, fishing rods.

Law of the Lever

Force multiplied by its arm (distance from the fulcrum) is equal to the resistance multiplied by its arm. F * d1 = R * d2

Inclined Plane

The inclined plane is used to move an object from one level to another higher level with less effort than if lifting it vertically. F * l = P * h

The inclined plane is used to move goods, avoid stairs, in tools, etc.

Screw

A screw is a piece that has a cylindrical or conical shape with a helical groove called a thread. It works with a nut.

The screw-nut mechanism transforms circular motion into rectilinear movement and is used as a fixation for detachable joints. It is used in jacks, corkscrews, clamps, wrenches, etc.

Screw Properties

  • Pitch (p): The distance between two consecutive threads.
  • Resistance (R): The force required to move a screw when it is engaged in a nut. P = R * 2πr / p
  • Threads: Can be left or right-handed. Can be single or multiple-start. Can have different shapes: triangular, trapezoidal, square, round, etc.

Thread Systems

  • Metric System: Uses millimeters as the unit. Example: M10 metric thread has a diameter of 10 mm.
  • Whitworth System: Uses inches as the unit. Example: W-3/8 is a Whitworth thread of 3/8 inch (9.52 mm).

Wheel

The wheel was a breakthrough invention that allowed the creation of the wheelbarrow, the treadmill, and the car.

Crank

The crank is a lever with one end fixed to an axis with rotary motion. Important applications include the crankshaft of vehicles, a boat’s rudder, and taps.

Winch

The winch consists of a rotating drum with a cable or rope wound around it and a crank at the ends.

Pulley

The pulley is a cylindrical piece with a central hole fixed on an axis that allows rotation. Pulleys can be flat, grooved, or toothed.

Types of Pulleys

  • Fixed Pulley: Fixed on its axis, can be considered a first-class lever (F = R).
  • Movable Pulley: The support point is located on the rope and not on the center. Usually used in combination with a fixed pulley.
  • Hoists: Combinations of fixed and movable pulleys that reduce the force required to overcome resistance.

Gear

A gear consists of two toothed wheels that mesh together.

Gears can have external or internal teeth.

Spur Gears

  • Pitch Diameter (d): The theoretical diameter where the teeth of two gears make contact. It is directly proportional to the module and the number of teeth. d = m * z
  • Circular Pitch (p): p = m * π
  • Module (m): The size of the teeth.
  • Addendum (a): The height of the tooth above the pitch circle.
  • Dedendum (a1): The depth of the tooth below the pitch circle. a1 = 1.25 * m
  • Tooth Height: a + a1
  • Outside Diameter (D): D = d + 2a
  • Root Diameter (di): di = d – 2a1