Mechanical Devices: Levers, Gears, Cams & Motion Systems
What Are Mechanical Mechanisms?
A mechanism is simply a device that takes an input motion and force and outputs a different motion and force. The purpose of a mechanism is to make a task easier to perform. The most commonly used mechanisms in mechanical systems include:
- Levers
- Linkages
- Cams
- Gears
- Pulleys
Understanding Levers
It’s important to understand how to calculate mechanical advantage obtained by using levers, the velocity ratio in levers and pulley systems, and the input and output speed when using gears.
The Basics of Levers
A lever is the simplest kind of mechanism. There are three different classes of levers. Common examples include the crowbar (Class 1), the wheelbarrow (Class 2), and a pair of tweezers (Class 3).
All levers are one of three types, usually called classes. The class of a lever depends on the relative position of the load, effort, and fulcrum:
- The load is the object you are trying to move.
- The effort is the force applied to move the load.
- The fulcrum (or pivot) is the point where the lever pivots.
Class 1 Levers
A Class 1 lever has the load and the effort on opposite sides of the fulcrum, like a seesaw. Examples of a Class 1 lever include a crowbar and pliers.
For example, it might take a force of 500N to lift a load directly. However, by using a lever—a rod with the fulcrum placed closer to the load than to the point of effort—it might only require a force of 100N. (Animation demonstration reference: Press play to see a demonstration.)
Class 2 Levers
A Class 2 lever has the load and the effort on the same side of the fulcrum, with the load nearer the fulcrum. Examples of a Class 2 lever include a nutcracker or a wheelbarrow.
In the diagram of a wheelbarrow, the wheel (fulcrum) helps share the weight of the load. This means it takes less effort to move a load in a wheelbarrow than to carry it directly.
Mechanical Advantage and Velocity Ratio in Levers
Class 1 and Class 2 levers both provide mechanical advantage. This means they allow you to move a large output load with a smaller input effort. Load and effort are forces and are measured in Newtons (N). Mechanical advantage (MA) is calculated as follows:
MA = Load ÷ Effort
In the example above, where the load = 500N and the effort = 100N, the mechanical advantage would be:
500N ÷ 100N = 5
Velocity Ratio
The mechanical advantage gained with Class 1 and Class 2 levers might seem like getting something for nothing: moving a large load with a small effort. However, the trade-off is that to make the effort smaller, the effort must move through a greater distance. For instance, in a Class 1 lever, you might need to push your end of the lever down further to move the load up a smaller distance. This trade-off is quantified by the velocity ratio (VR):
VR = Distance Moved by Effort ÷ Distance Moved by Load
Class 3 Levers
A Class 3 lever typically does not provide mechanical advantage in the same way as Class 1 and Class 2 levers (MA is often less than 1). In a Class 3 lever, the effort and the load are both on the same side of the fulcrum, but the effort is applied between the fulcrum and the load. This means more force is required for the effort than the force exerted by the load. However, these levers are useful for tasks requiring precision, speed, or a large range of motion, such as grabbing small, fiddly, or delicate objects. Common examples of Class 3 levers include tweezers or a fishing rod.
Tip: Learn the position of the load, effort, and fulcrum for each class of lever. Linking each class to a practical example will help you remember them.
Exploring Linkage Mechanisms
Linkages are mechanisms designed to direct force or motion precisely where it is needed. Linkages can be used to change:
- The direction of motion
- The type of motion
- The magnitude of a force
A linkage consists of a system of rods or other rigid materials connected by joints or pivots. The movement of each rod is constrained by both moving and fixed pivots. Consequently, the input at one end of a mechanical linkage will often differ from the output in terms of position, speed, direction, or other characteristics.
Types of Linkages
Reverse-Motion Linkage
A reverse-motion linkage changes the direction of motion. Often resembling a “Z” shape, this linkage features a central rod that moves around a central fixed pivot. Pushing or pulling the linkage in one direction creates an exact opposite motion in the other direction. If the fixed pivot were not central, it would result in a larger or smaller motion in the opposite direction.
Parallel-Motion Linkage
A parallel-motion linkage creates an identical parallel motion. Often resembling an “n” shape, the two side rods move around two fixed pivots, while the connecting top bar moves freely. Pushing or pulling the linkage in one direction produces an identical parallel motion at the other end of the linkage.
Bell-Crank Linkage
A bell-crank linkage changes the direction of movement through 90 degrees. It typically resembles an “L” shape or its mirror image. Pushing or pulling the linkage in one direction creates a corresponding motion at the other end, perpendicular to the input. For example, a bell-crank linkage can convert vertical movement into horizontal movement, as seen in some bicycle brake systems.
Treadle Linkage
A treadle linkage demonstrates how linkages can convert one type of motion into another. In a common setup, the rotary motion of a cam drives a parallel-motion linkage. This linkage, in turn, controls the identical side-to-side, or oscillating motion, of two connected components (e.g., in a sewing machine).
Understanding Cam Mechanisms
A cam is a shaped piece of material (often metal or plastic) fixed to a rotating shaft. A cam mechanism typically has three main parts:
- The Cam: The shaped rotating component.
- The Follower: The component that moves in response to the cam’s profile.
- The Camshaft: The shaft to which the cam is fixed.
The camshaft rotates continually, turning the cam. The follower is a rod or lever that rests on the edge (profile) of the turning cam. The follower is free to move in a specific path (e.g., up and down) but is usually constrained from moving in other directions by a slide or guide. Thus, the follower can perform three basic actions:
- Rise (move up or outwards)
- Fall (move down or inwards)
- Dwell (remain stationary)
The follower’s pattern of movement depends on the profile, or outside edge, of the cam that it follows. If the cam is perfectly round and the fixed shaft is in the center of the cam, the follower will dwell. But if the cam has a different shape, and/or the shaft is not central, the follower will rise or fall. How often and how quickly the follower moves is determined by the shape of the cam and the position of the shaft.
- Cams come in many different shapes—for example, pear-shaped, triangular, or square.
- The cam may have a chunk or chunks removed, so that the follower falls into a gap and is then pushed out again.
- Whatever the shape of the cam, positioning the shaft off-center will alter the behavior of the follower.
Types of Cams
Pear-Shaped Cam
The pear shape of this cam means that for approximately half the cycle, the follower will dwell. Then, as the pointed part (lobe) of the cam approaches the follower, the follower is pushed up (rises). As the point passes, the follower falls and then dwells again, completing the cycle.
Eccentric Cam
The eccentric cam is perfectly circular, but its rotating shaft is mounted off-center. This offset causes the cam to produce a smooth, symmetrical rise and fall motion in the follower. The follower typically never pauses to dwell with this type of cam.
Drop Cam (or Snail Cam)
With a drop cam (sometimes called a snail cam), the shaft is often central in a cam that is mostly circular but has a section abruptly “cut away” or shaped to create a sudden drop. The follower will dwell for most of the cycle, until it reaches the edge of this section and suddenly falls. It then rises again, often gradually, as the cam rotates back to its larger radius. The behavior of the follower can be significantly altered by changing the size of the cut-out portion or the smoothness of the incline leading to and from the drop.
Principles of Gear Mechanisms
Gears consist of toothed wheels fixed to shafts. The teeth of one gear interlock (mesh) with the teeth of another. As the first shaft (the driver shaft) rotates, motion is transmitted to the second shaft (the driven shaft). The motion output at the driven shaft can differ from the motion input at the driver shaft in terms of position, speed, direction, and torque.
A number of gears connected together are called a gear train. The input source (e.g., a motor) is connected to the driver gear, and the output (e.g., the wheel of a vehicle) is connected to the driven gear.
Common Gear Types and Calculations
Spur Gears
A simple gear train can be made up of a couple of spur gears. These are common gears (or cogs) that appear as wheels with teeth cut parallel to the gear’s axis of rotation, around the rim. (Reference to a photograph and diagram would be here.)
In technical drawings, the center of each gear is often shown by a cross. Each gear might be represented by two concentric circles, with the outer circle indicating the tips of the teeth. While individual teeth don’t always need to be drawn, the number of teeth is typically written next to the gear (e.g., 60 teeth and 15 teeth). Arrows indicate the direction of rotation. Note that with two externally meshing spur gears, they will rotate in opposite directions.
Gear Ratio and Output Speed
When two gears of different sizes are meshed, the smaller gear will rotate faster than the larger gear. The relationship between their speeds is defined by the gear ratio (often synonymous with velocity ratio in this context) and can be calculated using the number of teeth on each gear. The formula is:
Gear Ratio = Number of Teeth on Driven Gear ÷ Number of Teeth on Driver Gear
For example, if a smaller driver gear with 15 teeth meshes with a larger driven gear with 60 teeth, the gear ratio is:
Gear Ratio = 60 ÷ 15 = 4 (or 4:1)
This means the driver gear revolves four times to make the driven gear revolve once. If you know the gear ratio and the input speed at the driver gear, you can calculate the output speed at the driven gear using the formula:
Output Speed = Input Speed ÷ Gear Ratio
So, if the gear ratio is 4 and the driver gear is revolving at 200 revolutions per minute (rpm), then the output speed is:
Output Speed = 200 rpm ÷ 4 = 50 rpm
Advanced Gear Configurations
Compound Gear Train
When very large speed reductions (or increases) are required, several pairs of gears can be used in a compound gear train. In this setup, a gear on an intermediate shaft is driven by a gear on the input shaft, and another gear on the same intermediate shaft drives a gear on the output shaft. For example, a small gear drives a larger gear. This larger gear shares a shaft with a smaller gear, which in turn drives another larger gear. With each such stage, the speed can be significantly reduced (or torque increased).
Worm Gears
Another method for achieving large speed reductions is using a worm gear. A worm gear system consists of a “worm” (a shaft with a screw-like thread) that meshes with a “worm wheel” (a gear similar to a spur gear). The worm and worm wheel axes are typically at 90° to each other. Each time the worm shaft completes one revolution, the worm wheel advances by only one tooth (for a single-start worm). If the worm wheel has 50 teeth, this creates a gear ratio of 50:1. A key characteristic is that the worm can usually drive the worm wheel, but the worm wheel cannot drive the worm (it’s self-locking). This makes worm gears ideal for applications like hoists, where the load should not fall back when the motor stops. Worm gears are an excellent option when you need to change the direction of rotary motion by 90° and achieve significant speed reduction. (Reference to a photograph would be here.)
Bevel Gears
Bevel gears, similar to worm gears in one aspect, change the axis of rotation, often by 90°. However, unlike worm gears, bevel gears are cone-shaped. Their teeth are cut on the conical surface, allowing them to mesh when their axes intersect (typically at a right angle). Spur gears, in contrast, require parallel shafts.
Rack and Pinion
A rack and pinion system consists of a circular gear called the “pinion” that meshes with a linear gear called the “rack” (a flat bar with teeth). This mechanism converts rotary motion into linear motion, or vice versa. The pinion (driver cog) can either move along a stationary rack (as in a rack railway), or a rotating pinion can move the rack (as in automotive steering systems). (Reference to a diagram would be here.)
Pulley System Mechanics
Pulleys are wheels on an axle or shaft that are designed to support movement and change of direction of a taut cable or belt, or transfer of power between the shaft and cable or belt. Pulley systems are used to change speed, direction of rotation, or turning force (torque).
A basic pulley system for power transmission consists of two pulley wheels, each on a shaft, connected by a belt. This arrangement transmits rotary motion and force from the input (driver) shaft to the output (driven) shaft.
Velocity Ratio and Output Speed in Pulleys
If the pulley wheels are different sizes, the smaller pulley will spin faster than the larger one. The relationship between their speeds is determined by the velocity ratio (VR). This is calculated using the formula:
VR = Diameter of Driven Pulley ÷ Diameter of Driver Pulley
If you know the velocity ratio and the input speed of a pulley system, you can calculate the output speed using the formula:
Output Speed = Input Speed ÷ Velocity Ratio
Worked Example: Pulley Calculation
Let’s work out the velocity ratio and output speed for a pulley system with the following parameters (assuming a driver pulley of 40mm and a driven pulley of 120mm, with an input speed of 100rpm):
- Driver Pulley Diameter: 40mm
- Driven Pulley Diameter: 120mm
- Input Speed: 100 rpm
Calculation:
- Velocity Ratio (VR) = Diameter of Driven Pulley ÷ Diameter of Driver Pulley = 120mm ÷ 40mm = 3
- Output Speed = Input Speed ÷ VR = 100 rpm ÷ 3 = 33.3 rpm
Torque in Pulley Systems
The velocity ratio of a pulley system also influences the amount of turning force, or torque, transmitted from the driver pulley to the driven pulley. The formula is:
Output Torque = Input Torque × Velocity Ratio
This means if the driven pulley is larger (VR > 1, speed is reduced), the output torque is increased. Conversely, if the driven pulley is smaller (VR < 1, speed is increased), the output torque is decreased.
Pulley Drive Belts
Drive belts for pulley systems are commonly made from synthetic materials like neoprene and polyurethane, often with a V-shaped cross-section (V-belts) for better grip. It is possible to reverse the direction of rotation of the driven pulley by twisting the belt (forming a figure-eight) as it connects the input and output pulleys. Pulley belts offer the advantage over chains of not requiring lubrication, although they can be prone to slipping under high loads or if tension is incorrect, unlike a chain drive.
Fundamental Types of Motion in Mechanisms
There are four basic types of motion encountered in mechanical systems:
- Rotary motion: Turning around in a circle, such as a wheel turning.
- Linear motion: Moving in a straight line, such as the blade of a paper trimmer.
- Reciprocating motion: Moving backwards and forwards in a straight line, as in the action of cutting with a hand saw.
- Oscillating motion: Swinging from side to side along an arc, like a pendulum in a clock.
Many mechanisms are designed to convert one type of input motion into a different type of output motion. Below are some examples of mechanisms and the motion conversions they can achieve.
Motion Conversion Examples
Chain and Sprocket
A chain and sprocket system primarily transmits rotary motion between two sprockets but can also be part of a system that converts rotary motion to linear motion (e.g., a chain hoist) or vice versa. Other mechanisms for this conversion include a wheel-and-axle, rack-and-pinion, rope-and-pulley, and screw thread.
Cam-and-Follower
A cam-and-follower mechanism typically changes rotary motion (of the cam) to reciprocating or oscillating motion (of the follower). A crank-slider linkage can also achieve rotary to reciprocating conversion.
Peg-and-Slot (Geneva Drive or similar)
A peg-and-slot mechanism (like a Geneva drive or a simple crank-slot) can change continuous rotary motion to intermittent rotary motion or oscillating motion. A crank-slider linkage can also be used to change rotary motion to reciprocating motion.
Crank, Link, and Slider (Slider-Crank)
A crank, link, and slider mechanism (also known as a slider-crank) will change rotary motion (of the crank) to reciprocating motion (of the slider), or vice versa.
Rack-and-Pinion (Motion Conversion)
A rack-and-pinion system changes rotary motion (of the pinion) to linear motion (of the rack), or vice versa. A crank-slider mechanism can also convert rotary to reciprocating (a form of linear) motion. A cam-and-follower typically changes rotary motion to reciprocating/oscillating motion; converting reciprocating back to rotary with a cam is less common but possible with specific designs.
Combining Mechanical Systems and Sub-systems
Individual mechanisms or small systems can be combined to create more complex mechanical systems. For example, a cam turned by an electric motor can operate a microswitch, which in turn could be used to control an electrical circuit, such as turning a light on or off. By connecting two or more mechanical systems (sub-systems), engineers can achieve highly complex and precise movements or operations.