Understanding Mechanical Transmission Systems

The Mechanisms Explained

Mechanisms are essential components designed to transmit and transform energy and movement from a driving force to a receiver element. They allow humans to perform tasks with greater comfort and less effort.

Mechanisms are classified into:

• Transmission mechanisms of motion (linear or circular transmission).
• Mechanisms of transformation of movement (rectilinear to circular, or circular to rectilinear).

Lever

A lever is in equilibrium when the product of the applied force (F) and its distance from the fulcrum (d) equals the product of the resistance (R) and its distance from the fulcrum (r).

Formula: F · d = R · r

Types of Levers:

• First Class: The fulcrum is positioned between the applied force and the resistance.
• Second Class: The resistance is positioned between the fulcrum and the applied force.
• Third Class: The applied force is positioned between the fulcrum and the resistance.

Pulley Systems

• Fixed Pulley: The applied force (F) equals the resistance (R) it supports.
  Formula: F = R
• Movable Pulley: The applied force (F) is half the resistance (R).
  Formula: F = R / 2
• Hoist: Equilibrium is achieved when F = R / 2n, where 'n' is the number of movable pulleys.

Friction Wheels (Wheels of Friction)

The relationship between the rotation speeds of wheels or pulleys depends on their sizes.

Formula: N1 / N2 = D2 / D1. The ratio D1/D2 is called the transmission ratio.

(N1 and N2 indicate the speeds of the driving and driven wheels, respectively, and D1 and D2, their corresponding diameters.)

Gears or Toothed Wheels

The relationship between the rotation speeds of gears depends on the number of teeth each possesses.

Formula: N1 / N2 = Z2 / Z1. The transmission coefficient is the ratio Z1/Z2.

(N1 and N2 are the respective speeds of the wheels, and Z1 and Z2, the number of teeth.)

Worm Gear (Endless Screw)

In an endless screw system, the following equation applies:

Formula: N_spiral / N_wheel = Z_wheel. (N_spiral: spiral speed, N_wheel: wheel speed, Z_wheel: number of teeth of the wheel.)

Gear System with Chain

To calculate the relationship between the rotation speeds of the driving and driven wheels:

Formula: N2 / N1 = Z1 / Z2. (N1 and N2 are speeds, Z1 and Z2 are the number of teeth of the wheels.)

Speed Variation Systems

• Multiplier System: Transforms input speed (N1) into a higher output speed (N2).
  Formula: D1 > D2, N1 < N2.
• Constant Speed System: The input speed (N1) and output speed (N2) are equal.
  Formula: D1 = D2, N1 = N2.
• Reduction System: Transforms input speed (N1) into a lower output speed (N2).
  Formula: D1 < D2, N1 > N2.

Pulley Rail with Belt

The relationship between the rotation speeds of the driving wheel (1) and the driven wheel (4) depends on the pulley sizes.

Formula: N4 / N1 = (D1 · D3) / (D2 · D4). (N1 and N4 are speeds; D1, D2, D3, D4 are pulley diameters.)

Gear Train

The relationship between the rotation speeds of the driving wheels (1) and the driven wheels (4) depends on the number of teeth in the gear system.

Formula: N4 / N1 = (Z1 · Z3) / (Z2 · Z4). (N1, N4 are speeds; Z1, Z2, Z3, Z4 are teeth counts.)

Circular to Rectilinear Motion

The relationship between the rotational speed of a pinion and the linear advance speed of a rack is expressed by the following formula:

Formula: L = Z · P · N. (L: linear advance speed, Z: number of pinion teeth, P: pitch or distance between consecutive teeth, N: rotations per minute.)

Crank-Turn System

A turn is achieved when equilibrium is met in these equations.

Formula: F · r = R · d. If the ratio r/d is small, the crank will lift weights with little effort.

(F: applied force, R: resistance, r: radius of the crank arm, d: distance.)