Simple Machines and Mechanisms: How They Transmit and Transform Motion

Changing Forces and Motion Without Creating Energy

A simple machine can change the direction of a force or exchange force for distance. It does not produce energy: if less force is needed under ideal conditions, that force must act over a greater distance. Conversely, achieving more distance or speed at the output may require more force at the input. The ratio between output force and applied force is called mechanical advantage.

This exchange can be understood through work: a force acting while something moves transfers energy. In an ideal model, there are no losses, and input work equals output work. In a real machine, some energy is dissipated through friction or deformation; the weight of the parts also matters. For this reason, a ratio calculated using ideal geometry is not equivalent to a real load capacity.

Levers: Fulcrum, Force, and Resistance

A lever is a bar that rotates around a support or fulcrum. In the diagrams, F is the applied force, R the resistance or load, and △ the fulcrum. Lever arms are not simply distances along the bar: they are the perpendicular distances from the fulcrum to the forces' lines of action. Diagrams I, II, and III show the relative positions and directions of F and R; they do not represent the magnitudes of the forces to scale, nor do they necessarily show all the reactions at the fulcrum. Therefore, their graphical proportions do not have to match those in the numerical example.

The three classes are distinguished by the order of these elements:

• I: F—△—R. The fulcrum lies between the force and resistance; examples: seesaw and scissors.
• II: △—R—F. The resistance lies between the fulcrum and force; examples: wheelbarrow and nutcracker.
• III: △—F—R. The force lies between the fulcrum and resistance; tweezers are one example.

A first-class lever can favor force or distance, depending on the length of the arms: it does not always multiply force. A second-class lever can provide a force advantage; a third-class lever usually favors the distance traveled by the output end, at the cost of a lower force advantage.

In equilibrium, the moments on both sides of the fulcrum are equal. If the forces are perpendicular to the bar and its weight and friction are ignored, 20 N applied at 0.60 m can balance 60 N at 0.20 m: 20 × 0.60 = 60 × 0.20 = 12 N·m. The force advantage is 60/20 = 3. This is a hypothetical calculated example, not a measurement or a safe-load recommendation. N means newton, a unit of force; it is not a mass in kilograms.

Pulleys and Winches: Changing Direction or Distributing Effort

An ideal fixed pulley changes the direction of the force but does not reduce its magnitude: its mechanical advantage is 1. An ideal movable pulley, supported by two equal vertical segments of the same rope, requires half the force to support the load, but twice as much rope must be pulled in to raise it the same distance.

In a block and tackle, count the rope segments supporting the movable block, not the wheels. This interpretation assumes an ideal rope, frictionless pulleys, and suitable geometry; it cannot be used to infer a real lifting capacity. A crane can combine pulleys with a winch: the crank turns a drum that winds up rope. If the crank radius is large compared with the drum radius, the force required is reduced, in exchange for a greater distance traveled by the hand.

Ramps, Wedges, and Screws

An inclined plane makes it possible to reach a height by following a longer path; a ramp makes ascent easier by spreading the change in height over that distance. A wedge can be understood as one or two inclined planes that, when moved, separate or adjust parts; a doorstop is a simple example.

A screw is a helix based on the inclined plane. When turned, it can produce relative axial movement between the screw and a nut that does not rotate. How far it advances depends on the helix design: one turn does not mean the same displacement for every screw. Do not assume that any screw or mechanism locks on its own.

Transmissions: Carrying Rotation from One Part to Another

Circular transmissions carry rotation between components. In external friction wheels, the surfaces in contact rotate in opposite directions; they can slip, in which case the geometric ratio no longer exactly describes the actual speed. An open belt makes pulleys rotate in the same direction, while a crossed belt reverses the direction. External gears also rotate in opposite directions. An open chain and its toothed sprockets rotate in the same direction; the teeth prevent the slipping associated with a smooth belt, provided the chain meshes correctly.

To compare speeds, the transmission ratio is defined here as i = output speed / input speed, using magnitudes; the direction of rotation is described separately. For two compatible gears or two sprockets connected by a chain, i = input teeth / output teeth. For pulleys or friction wheels without slipping, i = effective input diameter / effective output diameter. “Effective” refers to the contact or pitch diameter, not necessarily the outer edge. If i is less than 1, the output reduces speed; if it is greater than 1, it increases speed; if it is 1, speed is maintained. Some manuals use the reciprocal, so check the definition before interpreting a value.

For example, a 15-tooth driving gear that drives a 45-tooth gear has i = 15/45 = 1/3. With an input speed of 60 rpm, the ideal output is 20 rpm. If the gears are reversed, i = 45/15 = 3; with the same input of 60 rpm, the ideal output is 180 rpm. These are calculated examples, not test results. A reducer can increase torque by reducing speed, but it does not increase power for free. A worm and wheel also transmit rotation between shafts; they can provide a large reduction depending on the design, but should not be assumed to always act as a brake or be self-locking. The ordinary rule of counting the teeth of two gears to calculate their ratio does not apply here.

Converting Rotation into Displacement or Reciprocating Motion

A rack and pinion converts rotation into linear displacement, as in the movement of a platform or a steering system. In a connecting rod and crank, a rotating crank is joined to a hinged connecting rod that pushes and pulls a guided slider: this transforms rotation into reciprocating motion, or can transmit motion in the reverse direction, depending on the setup. The guide is what forces the slider to follow a straight path; a connecting rod alone does not guarantee straight-line translation.

A cam transmits motion through its profile: as it rotates, it can raise, pause, or lower a follower. The follower must be kept in contact using a solution appropriate to the setup, such as a guide, a spring, or gravity. An eccentric is a circular disk whose axis is offset from its geometric center; as it rotates, it can produce reciprocating motion. The profile and setup determine the motion, so not every cam is oval-shaped or produces the same cycle.

A crankshaft combines several cranks fixed together on a shaft. Together with connecting rods, it relates the reciprocating motion of pistons to rotation, as in certain mechanisms in reciprocating engines; not all engines or clocks have a crankshaft. Mechanical clocks, on the other hand, may contain gear trains.

Observing Mechanisms with Classroom Models

Using a ruler resting on a fulcrum and light loads, students can try different positions for F and R. Before moving them, it is useful to predict which arrangement will require more force and which end will travel farther; then, the positions can be varied and the changes recorded in a sketch.

Using small pulleys or spools and rope, the group can count the rope segments supporting the load and compare how much rope is pulled with how far the load rises. A paper or cardboard automaton with a cam, or a disk connected to a connecting rod and slider, makes it possible to observe how rotation is converted into rising and lowering or reciprocating motion. The profile or positions of the parts can be varied, and predictions and observations recorded, without attributing measured educational outcomes to the activity.

For safety, an adult should prepare cuts and holes. Avoid exposed points and pinch hazards, use very light loads, and do not use motors or mains electricity. These models are not suitable for assessing a crane's strength, lifting people, or determining real load capacities.

Summary Table of Machines and Mechanisms