Lesson Note on Plotting Loci in Link Mechanisms for SS 2

Class: Senior Secondary School 2 (SS2 / SSS 2)
Term: 1st Term
Week: 5
Age: 16 years
Duration: 45 minutes
Subject: Technical Drawing
Curriculum Theme: Graphic Representation and Mechanisms
Previous Lesson: Meaning of Link Mechanism and Motions.
Topic: LINK MECHANISM
Subject Matter: Plotting loci of points on link mechanisms (tracing paths of moving joints)

Specific Objectives

By the end of the lesson, pupils should be able to:

Cognitive Domain:

• Define a link mechanism.
• Explain the term “locus of a point” in relation to mechanisms.
• Identify different types of link mechanisms.

Affective Domain:

• Appreciate the importance of plotting loci in understanding machine motion.
• Develop patience and precision when drawing complex curves.
• Show interest in the practical applications of link mechanisms.

Psychomotor Domain:

• Accurately plot the locus of a point on a given link mechanism.
• Use drawing instruments correctly to construct link mechanisms and their loci.
• Present neat and clear graphical solutions.

Social Domain:

• Collaborate with peers in discussing and solving graphical problems.

Reference Materials

The following resources were used in planning this lesson:

• Senior Secondary Schools Education Curriculum
• State Unified Scheme of Work
• Olaitan, A. B. (2018). Technical Drawing for Senior Secondary Schools. Learn Africa Plc.
• https://www.technicaldrawing.org/mechanisms
• https://www.engineeringdrawing.com/locus-of-points

Instructional Materials

The teacher will teach this lesson with the aid of:

• Posters showing various link mechanisms
• Charts illustrating plotted loci of points
• Working models of simple link mechanisms (e.g., four-bar, slider-crank)
• Drawing boards, T-squares, set squares, compasses, protractors, pencils, and erasers

Rationale for the Lesson

This lesson helps pupils understand how points on moving machine parts trace specific paths. Knowing how to plot these paths is important for designing and analyzing the motion of various machines and mechanical systems encountered in engineering and daily life.

Prerequisite/Previous Knowledge

Pupils have prior knowledge of basic geometric constructions, types of lines, and the use of drawing instruments. They also understand basic concepts of motion and points.

Lesson Content/Board Summary

LINK MECHANISM AND LOCUS OF POINTS

1. Definition of Link Mechanism

A link mechanism is an assembly of rigid bodies (links) connected by joints (pins or sliding pairs) that transmit motion and force. These mechanisms are fundamental components in many machines, converting one type of motion into another.

2. Definition of Locus of a Point

The locus of a point is the path traced by that point as it moves in space or on a plane. In link mechanisms, it refers to the curve traced by a specific point on one of the moving links as the mechanism operates.

3. Types of Link Mechanisms

The following are common types of link mechanisms:

• Four-Bar Mechanism: Consists of four links connected by four pin joints, where one link is fixed.
• Slider-Crank Mechanism: Consists of a crank, a connecting rod, and a slider, converting rotary motion to reciprocating motion or vice-versa.
• Toggle Mechanism: A variation of the four-bar mechanism designed to provide a large mechanical advantage at certain positions.
• Scotch Yoke Mechanism: Converts rotary motion into linear motion or vice-versa, often used in steam engines and internal combustion engines.

4. Steps for Plotting Loci of Points on Link Mechanisms

To plot the locus of a point on a link mechanism, follow these general steps:

1. Draw the Mechanism: Draw the mechanism in its initial position to a suitable scale.
2. Divide the Motion: Divide the input motion (e.g., crank rotation) into a convenient number of equal divisions (e.g., 12 or 16).
3. Locate Key Points: For each division, accurately draw the mechanism in its new position by locating all relevant joints and links.
4. Mark the Tracing Point: Identify the specific point on a link whose locus is to be traced. Mark its position for each of the divided steps.
5. Join the Points: Smoothly connect all the marked points to form the continuous curve of the locus. Use a French curve or freehand for accuracy.

5. Worked Example 1: Plotting the Locus of a Point on a Four-Bar Mechanism

Problem: A four-bar mechanism has a fixed link AD = 80mm. The crank AB = 30mm rotates clockwise. The coupler BC = 70mm and the follower CD = 60mm. Plot the locus of a point P on the coupler BC, where BP = 20mm and CP = 50mm, starting from a position where AB is horizontal to the right.

Solution Steps:

1. Step 1: Draw Fixed Link and Crank. Draw fixed link AD (80mm horizontal). From A, draw crank AB (30mm) horizontally to the right.
2. Step 2: Locate C. With B as center and radius BC (70mm), draw an arc. With D as center and radius CD (60mm), draw another arc to intersect the first arc at C. Join BC and CD.
3. Step 3: Locate P. On BC, locate point P such that BP = 20mm. Mark P. This is the first point on the locus.
4. Step 4: Divide Crank Rotation. Divide the crank’s full rotation (360°) into 12 equal parts (30° each). Label the positions of B as B1, B2, …, B12.
5. Step 5: Re-locate C and P for each position. For each position Bi:
   • From Bi, draw an arc with radius BC (70mm).
   • From D, draw an arc with radius CD (60mm) to intersect the previous arc. This gives Ci.
   • Join BiCi. On BiCi, locate Pi such that BiPi = 20mm (or CiPi = 50mm).
   • Mark Pi.
6. Step 6: Draw the Locus. Join all the marked points P1, P2, …, P12 with a smooth curve to obtain the locus of point P.

6. Worked Example 2: Plotting the Locus of a Point on a Slider-Crank Mechanism

Problem: A slider-crank mechanism has a crank OA = 40mm, rotating counter-clockwise. The connecting rod AB = 120mm. The slider moves along a horizontal line passing through O. Plot the locus of a point P on the connecting rod AB, 30mm from A.

Solution Steps:

1. Step 1: Draw Line of Stroke and Crank. Draw a horizontal line for the slider’s path through O. Draw crank OA (40mm) in its initial position (e.g., horizontal to the right).
2. Step 2: Locate B and P. With A as center and radius AB (120mm), draw an arc to intersect the line of stroke at B. On AB, locate point P such that AP = 30mm. Mark P. This is the first point on the locus.
3. Step 3: Divide Crank Rotation. Divide the crank’s full rotation (360°) into 12 equal parts (30° each). Label the positions of A as A1, A2, …, A12.
4. Step 4: Re-locate B and P for each position. For each position Ai:
   • From Ai, draw an arc with radius AB (120mm) to intersect the line of stroke. This gives Bi.
   • Join AiBi. On AiBi, locate Pi such that AiPi = 30mm.
   • Mark Pi.
5. Step 5: Draw the Locus. Join all the marked points P1, P2, …, P12 with a smooth curve to obtain the locus of point P.

Teaching Methods/Instructional Techniques

Discussion, Lecture, Demonstration, Question and Answer, Visual Aids

Instructional Procedures

Step 1: Introduction

Time: 5 minutes
Teaching Skill: Set Induction
Teacher’s Activity: The teacher greets the pupils and asks them to recall any machines they know that have moving parts, such as bicycle chains, engine parts, or door hinges. The teacher then introduces the topic of link mechanisms.
Pupils’ Activity: Pupils respond by mentioning machines with moving parts and pay attention to the introduction.
Learning Point: Pupils are introduced to the concept of moving parts in machines, setting the stage for understanding link mechanisms.

Step 2: Explanation of Link Mechanism

Time: 8 minutes
Teaching Skill: Explanation/Definition
Teacher’s Activity: The teacher defines a link mechanism using simple language and shows examples using posters or models. The teacher explains that links are rigid bodies and joints connect them to allow motion.
Pupils’ Activity: Pupils listen, observe the examples, and ask questions for clarification. They copy the definition into their notes.
Learning Point: Pupils understand what a link mechanism is and can identify its basic components.

Step 3: Explanation of Locus of a Point

Time: 7 minutes
Teaching Skill: Explanation/Illustration
Teacher’s Activity: The teacher defines “locus of a point” with practical examples, such as the path of a bicycle pedal or the tip of a wiper blade. The teacher explains that this path can be plotted graphically.
Pupils’ Activity: Pupils listen, relate the concept to real-life examples, and copy the definition.
Learning Point: Pupils understand the meaning of locus of a point in a mechanical context.

Step 4: Types of Link Mechanisms

Time: 7 minutes
Teaching Skill: Categorization/Illustration
Teacher’s Activity: The teacher discusses common types of link mechanisms such as four-bar, slider-crank, and toggle mechanisms, showing diagrams or models for each.
Pupils’ Activity: Pupils observe the different types and note their characteristics.
Learning Point: Pupils can identify and differentiate between various link mechanisms.

Step 5: Demonstration of Plotting Loci

Time: 10 minutes
Teaching Skill: Demonstration/Modelling
Teacher’s Activity: The teacher uses a large chart or the whiteboard to demonstrate step-by-step how to plot the locus of a point on a simple link mechanism (e.g., a four-bar mechanism or a slider-crank mechanism), following the steps outlined in the board summary. The teacher emphasizes accuracy and neatness.
Pupils’ Activity: Pupils pay close attention to the demonstration, asking questions about the procedure and the use of drawing instruments.
Learning Point: Pupils observe the practical steps involved in plotting the locus of a point.

Step 6: Guided Practice

Time: 5 minutes
Teaching Skill: Coaching/Supervision
Teacher’s Activity: The teacher provides a simplified problem or a partially drawn mechanism and guides pupils to start plotting a locus. The teacher moves around to provide individual assistance.
Pupils’ Activity: Pupils attempt to plot a simple locus under the teacher’s guidance, using their drawing instruments.
Learning Point: Pupils begin to apply the plotting techniques practically.

Step 7: Evaluation/Review

Time: 5 minutes
Teaching Skill: Questioning/Assessment
Teacher’s Activity: The teacher evaluates the learning by asking the following questions:

1. What is a link mechanism?
2. Define the term “locus of a point.”
3. Mention two common types of link mechanisms.
4. List the general steps involved in plotting the locus of a point on a link mechanism.

Pupils’ Activity: Pupils answer orally and in writing.

Learning Point: Pupils demonstrate understanding of the lesson.

Step 8: Conclusion

Time: 3 minutes
Teaching Skill: Summarization/Assignment
Teacher’s Activity: The teacher summarizes the key points of the lesson and assigns homework, which may include plotting a locus for a given mechanism from their textbook or a provided diagram.
Pupils’ Activity: Pupils listen to the summary and copy the homework assignment.
Learning Point: Pupils consolidate their learning and prepare for further practice.

Lesson Keywords

• Link – A rigid body in a mechanism.
• Mechanism – An assembly of links designed to transmit motion and force.
• Locus – The path traced by a moving point.
• Plotting – The graphical process of marking and connecting points to form a curve.
• Joint – A connection between links that allows relative motion.
• Path – The trajectory or curve followed by a moving point or body.

Differentiation

For pupils who grasp the concept quickly, the teacher can provide more complex link mechanism problems or ask them to explore different points on the same mechanism. For pupils needing more support, the teacher will offer one-on-one guidance, provide simpler examples, or pre-draw parts of the mechanism to reduce initial drawing load, focusing on the locus plotting aspect.

Note for teachers using this lesson plan

Ensure that pupils have a good grasp of basic geometric constructions before introducing complex link mechanisms. Emphasize the importance of accuracy in measurements and drawing, as small errors can significantly affect the plotted locus. Use physical models if available to help pupils visualize the motion of the links and the path of the point. Encourage pupils to use light construction lines and a sharp pencil for precision.