Lesson Note on Auxiliary View of Geometrical Solids: Drawing Auxiliary Plans and Elevations for SS 2

Class: Senior Secondary School 2 (SS2 / SSS 2)
Term: 2nd Term
Week: 3
Age: 16 years
Duration: 45 minutes
Subject: Technical Drawing
Curriculum Theme: Technical Drawing
Previous Lesson: Auxiliary View of Geometrical Solids: Meaning, Uses and Types.
Topic: AUXILIARY VIEW OF GEOMETRICAL SOLIDS
Subject Matter: Drawing first and second auxiliary elevations and plans (shaped blocks, geometrical solids)

Specific Objectives

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

Cognitive Domain:

• Define an auxiliary view.
• State the purpose of drawing auxiliary views.
• Identify the different types of auxiliary views.

Affective Domain:

• Appreciate the importance of auxiliary views in representing true shapes.
• Develop an interest in accurately projecting views of complex solids.

Psychomotor Domain:

• Accurately draw the first auxiliary elevation of a given solid.
• Accurately draw the second auxiliary plan of a given solid.

Social Domain:

• Collaborate effectively when working on drawing exercises.

Reference Materials

The following resources were used in planning this lesson:

• Senior Secondary Schools Education Curriculum
• State Unified Scheme of Work
• Engineering Drawing by N.D. Bhatt
• https://www.youtube.com/watch?v=1F568j0D4xI
• https://www.youtube.com/watch?v=F0m-1mQ-O5M

Instructional Materials

The teacher will teach this lesson with the aid of:

• Video clips showing auxiliary views
• Posters and charts illustrating auxiliary projections
• Drawing instruments (drawing board, T-square, set squares, pencils, compass, protractor)

Rationale for the Lesson

This lesson enables pupils to understand how to obtain the true shape and size of inclined surfaces on objects. This skill is important for accurately representing and interpreting engineering drawings of complex parts in various technical fields.

Prerequisite/Previous Knowledge

Pupils have basic knowledge of orthographic projections, including front elevation, plan, and end elevation.

Lesson Content/Board Summary

AUXILIARY VIEW OF GEOMETRICAL SOLIDS

Definition of Auxiliary View

An auxiliary view is an orthographic projection of an object onto an auxiliary plane. This plane is not parallel to any of the principal planes of projection (horizontal, frontal, or profile planes). Auxiliary views are used to show the true size and shape of inclined or oblique surfaces.

Purpose of Auxiliary Views

The main purpose of drawing auxiliary views is to obtain the true shape and size of a surface that appears foreshortened in the principal orthographic views (front, top, or side views).

Types of Auxiliary Views

• First Auxiliary View: Projected from a primary orthographic view (e.g., front elevation or plan) onto an auxiliary plane perpendicular to that primary view. It shows the true length of lines or true shape of surfaces that are inclined to one principal plane.
• Second Auxiliary View: Projected from a first auxiliary view onto a second auxiliary plane. This is used when a surface is oblique (inclined to all three principal planes) and requires two auxiliary projections to reveal its true shape.

Steps for Drawing a First Auxiliary Elevation

This involves projecting from the plan view to show the true shape of a surface inclined to the horizontal plane.

• Step 1: Draw the given orthographic views (e.g., front elevation and plan).
• Step 2: Draw a reference line (X1Y1) parallel to the inclined edge or surface in the plan view from which the auxiliary view is to be projected.
• Step 3: Project perpendicular lines from all critical points of the object in the plan view, across the X1Y1 line.
• Step 4: Measure distances from the original reference line (XY) in the front elevation to the corresponding points. Transfer these distances onto the projection lines from the X1Y1 line.
• Step 5: Connect the transferred points to complete the first auxiliary elevation.

Steps for Drawing a Second Auxiliary Plan

This involves projecting from a first auxiliary view to show the true shape of an oblique surface.

• Step 1: Draw the given orthographic views and the first auxiliary view.
• Step 2: Draw a second reference line (X2Y2) parallel to the inclined edge or surface in the first auxiliary view.
• Step 3: Project perpendicular lines from all critical points of the first auxiliary view across the X2Y2 line.
• Step 4: Measure distances from the reference line (X1Y1) in the first auxiliary view to the corresponding points in the primary view (e.g., plan). Transfer these distances onto the projection lines from the X2Y2 line.
• Step 5: Connect the transferred points to complete the second auxiliary plan.

Worked Example 1: Drawing a First Auxiliary Elevation

Given the front elevation and plan of a shaped block with an inclined surface, draw its first auxiliary elevation to show the true shape of the inclined surface.

• Step 1: Draw the given front elevation and plan views.
• Step 2: Identify the inclined surface in the plan view. Draw a reference line X1Y1 parallel to the edge of this inclined surface in the plan.
• Step 3: Project lines perpendicular to X1Y1 from all corners of the block in the plan view.
• Step 4: Take the height measurements from the front elevation (distances from the XY line to the corners). Transfer these heights from the X1Y1 line along the projection lines.
• Step 5: Join the points to form the first auxiliary elevation, highlighting the true shape of the inclined surface.

Worked Example 2: Drawing a Second Auxiliary Plan

Given the front elevation and plan of a truncated pyramid with an oblique cutting plane, draw a second auxiliary view to show the true shape of the cut surface.

• Step 1: Draw the given front elevation and plan.
• Step 2: Draw a first auxiliary elevation, projecting from the plan (or front elevation) such that one edge of the oblique surface appears as a point or true length.
• Step 3: Identify the oblique surface in the first auxiliary view. Draw a second reference line X2Y2 parallel to this oblique surface in the first auxiliary view.
• Step 4: Project lines perpendicular to X2Y2 from all corners of the oblique surface in the first auxiliary view.
• Step 5: Take measurements from the original reference line (e.g., XY in the plan) to the corresponding points in the plan view. Transfer these distances from the X2Y2 line along the projection lines.
• Step 6: Join the points to reveal the true shape of the oblique cut surface in the second auxiliary plan.

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, reviews the previous lesson on orthographic projections, and asks questions about the limitations of principal views in showing true shapes.
Pupils’ Activity: Pupils respond to questions and recall previous knowledge.
Learning Point: Pupils connect previous knowledge to the new topic and understand the need for auxiliary views.

Step 2: Explanation of Auxiliary Views

Time: 8 minutes
Teaching Skill: Explanation/Definition
Teacher’s Activity: The teacher defines an auxiliary view, explains its purpose, and introduces the two main types (first and second auxiliary views) using charts and diagrams.
Pupils’ Activity: Pupils listen attentively, ask clarifying questions, and take notes on the definitions and purposes.
Learning Point: Pupils understand what an auxiliary view is and why it is used.

Step 3: Demonstration of First Auxiliary Elevation

Time: 10 minutes
Teaching Skill: Demonstration/Modelling
Teacher’s Activity: The teacher demonstrates, using a drawing board and instruments, how to draw a first auxiliary elevation of a simple shaped block with an inclined surface, following the steps outlined in the board summary. Video clips may be used.
Pupils’ Activity: Pupils observe the demonstration carefully, noting the steps and techniques for projection.
Learning Point: Pupils learn the practical steps involved in constructing a first auxiliary elevation.

Step 4: Practice of First Auxiliary View

Time: 7 minutes
Teaching Skill: Guided Practice
Teacher’s Activity: The teacher provides a simple exercise for pupils to attempt drawing a first auxiliary view. The teacher moves around to provide guidance and correct common errors.
Pupils’ Activity: Pupils attempt to draw the first auxiliary view under the teacher’s supervision.
Learning Point: Pupils apply the learned steps to draw a first auxiliary elevation.

Step 5: Demonstration of Second Auxiliary Plan

Time: 7 minutes
Teaching Skill: Demonstration/Modelling
Teacher’s Activity: The teacher demonstrates how to draw a second auxiliary plan of an object with an oblique surface, emphasizing the need for a first auxiliary view as an intermediate step.
Pupils’ Activity: Pupils watch the demonstration, paying attention to the increased complexity and additional projection steps.
Learning Point: Pupils understand the process for constructing a second auxiliary plan for oblique surfaces.

Step 6: Practice of Second Auxiliary View

Time: 3 minutes
Teaching Skill: Guided Practice
Teacher’s Activity: The teacher assigns a short exercise for pupils to begin drawing a second auxiliary view, offering support as needed.
Pupils’ Activity: Pupils start working on the second auxiliary view, applying the demonstrated techniques.
Learning Point: Pupils gain initial experience in drawing second auxiliary views.

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 an auxiliary view?
2. State two purposes of drawing auxiliary views.
3. Explain the difference between a first and a second auxiliary view.
4. Briefly describe the steps to draw a first auxiliary elevation.

Pupils’ Activity: Pupils answer orally and in writing.

Learning Point: Pupils demonstrate understanding of the lesson.

Step 8: Conclusion

Time: 2 minutes
Teaching Skill: Summarizing
Teacher’s Activity: The teacher summarizes the key points of the lesson, reiterating the importance of auxiliary views in technical drawing and assigning homework to practice drawing various auxiliary views.
Pupils’ Activity: Pupils listen to the summary and copy down the homework assignment.
Learning Point: Pupils consolidate their understanding and are prepared for further practice.

Lesson Keywords

• Auxiliary View – A view projected onto a plane that is not one of the principal planes.
• First Auxiliary View – Projected from a primary orthographic view.
• Second Auxiliary View – Projected from a first auxiliary view.
• True Shape – The actual shape and size of a surface.
• Oblique Surface – A surface inclined to all three principal planes.

Differentiation

For struggling pupils, the teacher will provide pre-drawn orthographic views to focus only on the projection steps for auxiliary views. Advanced pupils will be challenged with more complex geometrical solids or objects requiring multiple auxiliary views.

Note for teachers using this lesson plan

Ensure pupils have a solid understanding of basic orthographic projections before introducing auxiliary views. Emphasize the importance of accuracy in projection lines and measurements. Use physical models or 3D software demonstrations to help pupils visualize the auxiliary planes and projections.