Lesson Notes By Weeks and Term v5 - Grade 8

Lesson Video

This page supports the lesson note with a companion video and a short classroom-ready summary.

For class groups and homework, share this lesson page so learners also get the summary, objectives, and full lesson context.

Performance objectives

• Identify components of a mechanical system (input, process, output).
• Explain the function of common linkages like the bell crank and crank-slider.
• Sketch and label basic linkage diagrams.
• Construct simple models of linkages.
• Analyze a real-world device that uses a linkage system.

Lesson summary

This week, we delve into the fascinating world of mechanical systems and linkages. These are the fundamental building blocks that make many machines and devices work. Understanding how linkages operate is crucial because they are used extensively in everyday life, from the simple mechanism that opens and closes a gate in a township to complex machinery used in factories and vehicles throughout South Africa. Consider the windscreen wipers on a taxi, the suspension of a bakkie, or the mechanism that allows an excavator on a construction site to move its arm – all rely on linkages.

Lesson notes

What is a Mechanical System? A mechanical system is a collection of interconnected parts that work together to perform a specific task. It takes an input, processes it, and produces an output. A mechanical system can also incorporate feedback to monitor and adjust its performance.

Consider a bicycle: the input is the force you apply to the pedals, the process involves the chain and gears transferring that force to the wheels, and the output is the bicycle moving forward.

Input: The energy or signal that enters the system.

Process: What the system does to the input.

Output: The result of the process.

Feedback: Information about the output that is used to adjust the input or process. (We will delve deeper into feedback in later weeks, but it's important to introduce the concept now). What are Linkages? A linkage is a mechanical system composed of rigid bars (links) connected by joints (pivots or hinges) that allow relative motion. Linkages are used to transmit and transform motion and force. They can convert rotary motion to linear motion, change the direction of motion, or amplify force. The arrangement of the links and pivots determines the type of motion produced.

Common Types of Linkages: Bell Crank: The bell crank linkage consists of two links connected at a pivot point, typically forming a right angle or an "L" shape. When one link is moved, the other link also moves, changing the direction of the force by 90 degrees.

Example: A traditional hand-operated water pump found in rural communities. The handle acts as one link, and the rod connected to the pump piston acts as the other. Pulling the handle down causes the rod to move upwards, drawing water.

Crank-Slider: This linkage converts rotary motion into linear motion, or vice versa. It consists of a rotating crank (a circular link), a connecting rod, and a slider that moves linearly.

Example: The engine of a car or a generator. The rotating crankshaft (crank) is connected to the piston (slider) by a connecting rod. The rotation of the crankshaft causes the piston to move up and down within the cylinder, which drives the car. A similar principle is found in older sewing machines that use foot pedal power.

Four-Bar Linkage: This is one of the most fundamental and versatile linkages. It consists of four links connected by four pivots. By varying the lengths of the links and the location of the pivots, a wide range of motions can be achieved. A crucial aspect of four-bar linkages is Grashof's law, which determines whether at least one link will be able to fully rotate. Grashof's law states that for a four-bar linkage, the sum of the shortest and longest link lengths must be less than or equal to the sum of the remaining two link lengths. If this condition is met, then at least one link will be able to fully rotate.

Example: The suspension system of a vehicle. The four-bar linkage ensures the wheel moves vertically while maintaining the desired wheel alignment and stability. Another example is the mechanism that opens and closes a gate – often constructed using a simple four-bar linkage to provide a smooth and controlled motion.

Worked example

Example 1: Calculating the velocity ratio of a bell crank.

Imagine a bell crank used in a gate mechanism. The input arm (the one you push) is 30cm long, and the output arm (connected to the gate latch) is 15cm long. What is the velocity ratio?

Velocity Ratio (VR) = Distance moved by input / Distance moved by output

Since the arms are linked, the angular displacement will be the same.

However, the linear distance moved at the end of each arm will be different. We can approximate the distance moved by each arm as a fraction of a circle's circumference.