Understanding Simple Machines, Mechanisms, and Mechanical Elements

Posted on Nov 22, 2024 in Technology

Mesopotamia and the Dawn of Simple Machines

Around 3500 BC, Mesopotamian philosophers identified five simple machines: the wedge, inclined plane, wheel, and lever. All early machines were based on these or their combinations. The fundamental principle: the driving force equals the resisting force.

When a force acts on an object, it tends to deform it. This deformation depends on the force’s direction, orientation, and application point. Machine elements experience various efforts:

  • Traction (lengthening)
  • Compression (reduction)
  • Flexion (bending)
  • Torsion (twisting)
  • Cutting/Shearing (breaking through a surface)

The moment of a force about a point is the product of the force and the distance from the point to the force’s line of action (M = F × R). Power (P) relates to torque (M) and angular velocity (ω) as P = M × ω.

Hachette’s Classification of Mechanisms

In 1811, Hachette classified mechanisms based on their function within a machine:

  • Receivers: Obtain motion from a prime mover.
  • Communicators: Transmit motion.
  • Modifiers: Transform motion type.
  • Regulators: Control motion.
  • Stands: House and support components.
  • Operators: Produce the final effect.

A machine is a set of mechanisms working together to produce a desired outcome.

Machine Types

1. Drive Machines (Energy Sources)

  • Movers: Convert energy (e.g., electrical) for machine use.
  • Motor Side: Directly drive the machine. Energy sources include:
    • Muscle Power: From humans or animals, used in transportation.
    • Thermal Energy: External combustion (steam engines) and internal combustion engines (diesel, gasoline, turbines).
    • Electricity: Electric motors and electromagnets.

2. Machine Operators

Utilize power to achieve an effect, including conveyors, modifiers (milling, lathe), and specialized devices (calculators, computers).

Machine Elements

Shafts

Cylindrical elements supporting rotating parts. They experience bending and shear stresses but don’t transmit power.

  • Fixed Shafts: Stationary, allowing supported parts to rotate.
  • Rotating Shafts: Rotate with connected components.
    • Solid Shafts: Deform gradually under bending.
    • Hollow Shafts: Offer better resistance to bending.

Trees (Power Transmission Shafts)

Cylindrical or non-cylindrical elements transmitting power and torque. They experience torsion and flexion.

Tree Couplings

  • Rigid (Aligned):
    • Flange Couplings: Two half-flanges bolted together.
    • Conical Couplings: Tapered pieces pressed together.
  • Mobile (Non-aligned):
    • Gasket Couplings: Flexible material (rubber, neoprene) absorbing misalignment up to 15°.
    • Cardan/Universal Joints: Transmit motion between shafts at angles up to 45° using yokes and a cross. Constant Velocity (CV) joints prevent oscillations.
    • Oldham Couplings: Use a disc between two shafts with slots to transmit motion between parallel, offset shafts.
    • Sliding Spline Shafts: Allow length variation.

Gearing

Transmits motion through friction, requiring an axial force to prevent slippage. The driving wheel (pinion) is smaller; driven wheel parameters are capitalized. Power transmission: P = 2πnrFμ (P: power, n: pinion speed, r: pinion radius, μ: friction coefficient, F: force).

External Gearing

: This consists of two disks that are in contact with the outer surfaces. This contact is made by pressure. Rotate in opposite directions. The wheelbase is E = R + r = D + d / 2. Ratios (L): is the ratio of the wheel angular velocity and angular velocity of the pinion:L = N / n. L> 1 (N> n) – speed multiplier, L – Speed, L = 1 (n = N). The tangential speed of the wheels is the same as v = V n × r = N × R i = N / n = r / R = d / D. 1.Ruedas internal friction: this consists of two disks that are in contact with the outer surface of one and the interior of another. Rotate in the same direction. The wheelbase is E = Rr = Dd / 2. Ratios (L): is the ratio between the angular velocity of the wheel and the angular velocity of pinion: i = N / n = r / R = d / D. 2. stumps gearing: transmit motion between shafts whose processes are cut. They are shaped like truncated cone at any point of contact loved wheels, its tangential velocity is the same: i = N / n = r / R = d / D = Tg.
Pulley: grooved wheel is used in transmissions via mail and e: is the flexible string or cord attached to its ends for transmitting the torque from one wheel to another. The belt: the mechanism that connects two pulleys and transmits the movement from one to another. It employs more than friction in the wheels because they have more surface friction and can transmit greater efforts. For optimal performance, the belts should be tensioned properly, exercising proper axial force. Its gear ratio is i = N / n = r / R = d / D.

Section:-Trapezoidal (are made of rubber and acquire high speed, industrial uses)-Flat or rectangular (are made of leather and acquire great powers within the cassette or to transmit the motion between nonparallel axes)-round or circular (acquire small forces in the old sewing machines or for transmitting motion between axes not parallel).
Gears: used to transmit large power and consequent high torque. It has two gears. The driver is called pinion wheel and driven wheel. Teeth: – Straight (parallel to the axis of the wheel. They are noisy, cause vibration, but are inexpensive. They have a distinctive profile called profile enclosure that makes the strength of Thrust bearing the same direction and that the transmission ratio is constant. They are used when the power to be transmitted and the number of revolutions that turn is not very large.)-Spiral (are inclined to the axis. They are a little noisy and produce little vibration, but they are my expensive. They are used when the power to be transmitted and the number of revolutions that turn is very large)-Gears in v (to compensate the axial forces, using two gears whose teeth form a complementary angle.
Parameters of a gear wheel – pitch diameter (dp): the diameter would correspond to a friction wheel that has the same gear ratio. For two wheel gears, their pitch circles must be tangent. –Diameter (in) is the one that corresponds to the outer circumference of the teeth. “Inside diameter (ID) is the one that corresponds to the inner circumference of the teeth. Module (m): is the ratio between the pitch diameter and number of teeth m = dp / z. This standard (measured in mm). – Step circular (p): is the arc measured along the pitch circle between two homologous sides of the tooth row. This standard (measured in mm). For two gear wheels, must have the same module. L = Lp / 2 = ðdp / 2 = mð of +2 m di = dp = dp-2, 5m Lp-length of the pitch circle. Addendum height h1 = re -rp = m decentum Height: h2 = rp-ri = 1.25 m Height tooth: h = h1 + h2 tooth length: b = 10m tooth thickness S = 19/40p Hollow Tooth W = 21/40p.
Performance of a machine or mechanism: not all power or energy transmitted from the motor reaches the final tree where needed. Part of it is lost due to friction, slip and design elements. When the tree tour with a couple or moment M, is seated on its base, thus cause friction. Fr = MN Mr = Fr × R Mu = M-Mr = M-M-?NR Fr = Pt = Ps = MW Pu = (M-?NR) × W: = (M-?NR) × W / MW = 1-MNR / M. Fr-friction force (N) N-normal force (N) M-torque (NM) Mr-frictional torque (NM) coefficient of friction ?-(0-1) p-power (W) W-angular velocity (rad / s) R-radius (m). The shape of the teeth of spur gears causes the force exerted on the pinion wheel is not horizontal but at an angle of 20 ° pressure angle called. The transmit power is Fx = F × cos20 º F = 0.94 Fy = F × sin20 º (normal) × friction, the yield for each pair of gears is 94%.
Transformers mechanical elements of movement: 1.Piñon-zipper (loop? Rectilinear) is a gear which comprises a wheel called a pinion and a rack called infinite radius of trapezoidal teeth. “The rack and pinion turns this down, the pinion moves. It is used in lathes (machines and tools. “The rack and pinion moves this fixed, the pinion rotates. Currently used mechanical calculators.” The pinion rotates without moving and the zipper is moved. It is for drill press, automobile steering and automatic garage doors. 2.Tornillo-nut: the screw rotates, the nut holding. If an inclined plane is wrapped on a cylinder, the ramp shape of the screw propeller on the propeller and if you paste a triangle rubber will have a very long thread. Its uses are lifting (of a car jack), hold objects (vise) and place objects accurately (binoculars). The time needed to lift a load is: M = Qp / 2ð.M-moment (Nm) p-screw thread pitch (m) q-load (N). 3.Excentrica (loop)? (Rectilinear alternate): a disc-shaped piece or cylinder or cylinder rotating about an axis that coincides with the geometric axis. The wheelbase is called eccentricity. They produce a smooth continuous motion a follower called simple harmonic motion. 4.Leva: it is irregularly shaped piece that rotates around an axis, transforming a circular Movimas alternative rectilinear movement of a follower or a vastajo.
Crank rod mechanism: the crank is a piece that goes around and the crank is a piece that is attached to the handle and to complete an alternative rectilinear motion. It turns circular motion into a linear or vice versa. If you turn the crank, the piston moves forward and backward, and when you push or pull the plunger, the handle or spin. Motor driven: MC? MRA MRA? MCU. 1.Biela-crank-piston: the conductive element is the wheel and driving the plunger. Fixed to the plunger, place the functional element of the machine. 2.Biela-crank-shaft: Used primarily in internal combustion engines. It is divided into 4 stages:-Admission: open the inlet valve (va), the piston moves from top dead center (TDC) to bottom (PMI) driven by the crankshaft and air enters. The crankshaft passes 180 degrees, just the 1st phase. “The piston goes from pmi pms dragged the crankshaft, the air is compressed and the crankshaft has moved 180 degrees. -Expansion: When the piston reached TDC, the spark, combustion occurs and the gases push the piston down: The crankshaft passes 180 degrees (no work). “Escape: the crankshaft rotates 180 degrees and the passage of the pms is pmi opens the exhaust valve (ve) and the gases flow out.
Ratchet: This consists of a toothed wheel and another piece scraper, which gets between the teeth of the wheel, the effect of a spring or by their own weight and allow the rotation of a shaft in one direction but not in the opposite direction . There are two types: reversible (can vary the effect of blockade as interested in every time) and non-reversible (always block the direction of rotation in the same direction).
Flywheel: is an element that is placed on a shaft or a shaft to allow the drive shaft axis move the resistant and not vice versa. It consists of two wheels, one with a series of rollers or balls and springs. When the drive wheel rotates, it drags the wheel thanks to the rollers or balls interlock between the two, making solidarity. Its main uses are: rear-wheel bicycle and car starter.