Lesson Notes By Weeks and Term v5 - Grade 8

Lesson Video

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Performance objectives

• Define a mechanical system and a linkage with examples.
• Identify and describe different types of linkages.
• Explain how linkages change the direction, force, or speed of motion.
• Design a simple mechanical system using a linkage.
• Analyze motion and force in a simple linkage system.

Lesson summary

This week, we delve into the fascinating world of mechanical systems and linkages. Mechanical systems are all around us, from the simple scissors we use to cut paper to the complex suspension systems in our cars and the intricate mechanisms that control the movements of heavy machinery used in South African mines and factories. Understanding how these systems work helps us appreciate the ingenuity of engineering and empowers us to design and build our own solutions to real-world problems. Knowing about linkages is crucial because they are a fundamental building block in many machines, allowing us to transfer motion and force in useful ways.

Lesson notes

What is a Mechanical System? A mechanical system is a combination of parts or components that work together to perform a specific function. These systems rely on mechanical power and the movement of components to achieve their goals. Mechanical systems use forces and motion to transfer energy and perform tasks. Examples include a bicycle, a car engine, a crane, and even a pair of scissors. What is a Linkage? A linkage is a mechanical system consisting of rigid bars or links connected by joints that allow relative motion. Linkages are used to transmit and transform motion and force. They can change the direction of motion, amplify force, or convert rotary motion to linear motion (or vice versa). Essentially, a linkage system is a series of connected bars which converts input movement and forces into a desired output movement and force.

Types of Linkages: Bell Crank Linkage: A bell crank linkage is a type of linkage that consists of two levers pivoted at a common point. It's typically L-shaped. This linkage is primarily used to change the direction of motion, usually by 90 degrees. For example, the brake system in an old bicycle or the mechanism for operating a gate.

Example: Imagine a security gate at a local shop. Pulling a lever down could rotate a bell crank to lift the gate up (or slide it sideways). The input (pulling down) results in a different direction for the output (gate lifting or sliding).

Push-Pull Linkage (Connecting Rod): This linkage is a simple straight bar that transmits force and motion linearly between two points. It converts rotary motion to linear motion, or vice-versa.

Example: A piston in a car engine uses a connecting rod (push-pull linkage) to convert the linear motion of the piston into the rotary motion of the crankshaft. This happens in many vehicles on our South African roads.

Four-Bar Linkage: This is one of the most versatile and widely used linkages. It consists of four bars connected by four joints (pivots). By varying the lengths of the bars and the point of actuation (where the input force is applied), a wide range of motion patterns can be achieved. One bar is typically fixed (the ground link). The other three are called the crank (input link), the coupler, and the follower (output link).

Example: A simple example is a windscreen wiper system in a car. The motor rotates a crank which drives the four-bar linkage, resulting in the back-and-forth motion of the wipers. Another example might be the mechanism to lower and raise the buckets of a construction vehicle.

Slider-Crank Linkage: This linkage consists of a crank, a connecting rod, and a slider. The crank rotates, causing the connecting rod to push or pull the slider back and forth in a linear path.

Example: The internal combustion engine relies heavily on the slider-crank mechanism. The movement of the piston inside a cylinder is converted into rotational movement of the crankshaft. This is the core working principle of many cars and bakkies driven every day.

How Linkages Change Motion and Force: Linkages don't just move things; they can also modify the motion or force.

Here's how: Changing Direction: As seen in the bell crank example, linkages can change the direction of motion. A horizontal force can be converted into a vertical force. Changing Magnitude of Force (Mechanical Advantage): Linkages can provide mechanical advantage, meaning they can multiply the force applied. This is particularly useful when you need to move heavy objects or overcome resistance. The trade-off for increased force is often a reduction in distance or speed.

Example: A lever (which can be part of a linkage) can be used to lift a heavy rock. By positioning the fulcrum (pivot point) closer to the rock, you need to apply less force to lift it, but you need to move the lever a greater distance. This principle is used in many hand-operated water pumps found in rural communities.

Changing Speed: Linkages can also change the speed of motion. If a small input motion results in a large output motion, the linkage is increasing speed.

Worked example

Problem: You need to design a mechanism to open and close a small gate used to control water flow in an irrigation system. The handle to operate the gate will be at right angles to the gate itself.

Solution: A bell crank linkage would be suitable. One arm of the bell crank would be connected to the handle, and the other arm would be connected to the gate. When the handle is rotated, the bell crank rotates, causing the gate to open or close.

Problem: Design a mechanism to convert the rotational motion of a hand crank into the back-and-forth motion of a small saw.

Solution: A slider-crank mechanism would be ideal. The hand crank would rotate the crank in the linkage. The connecting rod would then push and pull the slider (the saw) back and forth.

Problem: You want to design a simple exercise machine where pushing a foot pedal causes a rotating wheel to spin.

Solution: A four-bar linkage can be used. The foot pedal acts as one link, the frame of the machine acts as the ground link, a connecting rod acts as the coupler, and the rotating wheel acts as the follower. The movement of the pedal will translate into the rotary movement of the wheel.

Guided Practice (With Solutions)