Archimedean Spiral, Hyperbola, Link Mechanisms Technical Drawing SS 2 First Term Lesson Notes Week 1 and 2

Lesson Plan: Technical Drawing

Subject: Technical Drawing

Class: SS2

Term: First Term

Week: 1 and 2

Age: 16-17 years

Topic: Special Curves (Loci)

Sub-topic: Archimedean Spiral, Hyperbola, Link Mechanisms

Duration: 80 minutes

Behavioural Objectives:

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

1. Define various loci, e.g., Archimedean spiral, hyperbola.
2. Construct various loci.
3. State the practical applications of each loci.
4. Plot the loci of points on different link mechanisms.

Keywords:

Loci, Archimedean Spiral, Hyperbola, Link Mechanisms

Set Induction:

Begin with a discussion on common curves seen in daily life, such as spirals in snail shells and curves in bridges.

Entry Behaviour:

Students have basic knowledge of geometric shapes and drawing tools.

Learning Resources and Materials:

• Drawing instruments (compass, protractor, T-square, set square, divider, scale, French curve, straight edge)
• Drawing board and paper
• Models of curves
• Charts and posters

Building Background/Connection to Prior Knowledge:

Discuss how geometric shapes are used in previous topics and real-life applications.

Embedded Core Skills:

• Critical thinking and problem solving
• Communication and collaboration
• Leadership and personal development

Learning Materials:

• Lagos State Scheme of Work for Technical Drawing
• Drawing manuals and textbooks
• Online resources (e.g., slideshare.net)

Instructional Materials:

• Protractor, compass, T-square, set square, divider, scale, French curve, straight edge
• Drawing board, drawing paper, models, charts, posters

Content:

Definitions and Constructions:

1. Archimedean Spiral:
   • Definition: The Archimedean spiral is a type of spiral named after the Greek mathematician Archimedes. It is defined as a curve that moves away from a fixed point with a constant speed along a line which rotates with constant angular velocity.
   • Construction: To draw an Archimedean spiral, use a compass to draw multiple circles with increasing radii from a common center. Each radius should increase by a consistent increment. Connect the points where each circle intersects a radial line extending from the center.
   • Applications: Archimedean spirals are used in mechanical devices like spiral springs and also in graphic design and architecture for aesthetic curves.
2. Hyperbola:
   • Definition: A hyperbola is a type of smooth curve lying in a plane, defined by its geometric properties or by equations that satisfy certain conditions. It consists of two separate curves called branches that mirror each other and open in opposite directions.
   • Construction: To construct a hyperbola, start with two fixed points (foci) and a constant difference of distances from any point on the curve to the foci. Using set squares and a ruler, plot points equidistant from the central axis ensuring the distances to the foci are maintained.
   • Applications: Hyperbolas are found in various fields such as physics (trajectory of particles), engineering (cooling towers), and navigation (radio signals).
3. Link Mechanisms:
   • Definition: Link mechanisms refer to the paths or loci traced by a point on a moving link within a mechanism. These paths can be complex and are crucial in designing mechanical systems.
   • Construction: To plot the loci of points on link mechanisms, use a divider to measure and mark points along the movement path of the mechanism. This involves understanding the geometry and movement constraints of the mechanism.
   • Applications: Link mechanisms are used in various machines, including engines, robotic arms, and manufacturing equipment, to create desired movements and outputs.

Evaluation (Fill-in-the-Blank Questions):

1. The ________ spiral has equal distances between its coils.
   a) Archimedean
   b) Parabolic
   c) Elliptical
   d) Circular
2. A hyperbola is defined by its ________ properties.
   a) geometric
   b) arithmetic
   c) algebraic
   d) trigonometric
3. The path traced by a point on a moving link is called ________.
   a) trajectory
   b) locus
   c) hyperbola
   d) arc
4. The ________ is used to draw circles and arcs.
   a) compass
   b) protractor
   c) T-square
   d) set square
5. A French curve is used to draw ________ lines.
   a) straight
   b) curved
   c) parallel
   d) perpendicular
6. The point where a spiral starts is called the ________.
   a) vertex
   b) focus
   c) origin
   d) end
7. Hyperbolas have two branches that open in ________ directions.
   a) same
   b) different
   c) parallel
   d) perpendicular
8. The Archimedean spiral is named after the mathematician ________.
   a) Pythagoras
   b) Archimedes
   c) Euclid
   d) Newton
9. Link mechanisms are used to create ________ movements in machines.
   a) random
   b) desired
   c) chaotic
   d) unpredictable
10. The constant difference in distances from any point on a hyperbola to the foci is called the ________.
    a) radius
    b) diameter
    c) constant
    d) distance
11. The instrument used to measure angles is called a ________.
    a) compass
    b) protractor
    c) T-square
    d) ruler
12. A hyperbola is an example of a ________ curve.
    a) linear
    b) quadratic
    c) conic
    d) cubic
13. The Archimedean spiral is used in ________ devices like springs.
    a) electrical
    b) mechanical
    c) optical
    d) chemical
14. The points on a hyperbola are ________ from the center axis.
    a) equidistant
    b) random
    c) unequal
    d) variable
15. The Archimedean spiral increases in radius by a ________ increment.
    a) random
    b) constant
    c) variable
    d) geometric

Class Activity Discussion (FAQs):

1. What is an Archimedean spiral?
   • It’s a spiral with equal distances between its coils.
2. How do you construct a hyperbola?
   • By plotting points equidistant from a central axis using set squares and a ruler.
3. What are link mechanisms?
   • They are paths traced by a point on a moving link in a mechanism.
4. What tools are used for drawing circles?
   • Compass and divider.
5. Why are French curves important?
   • They help draw smooth curves that can’t be made with a compass or straight edge.
6. What is the use of a protractor?
   • It is used to measure and draw angles.
7. How is a hyperbola different from a circle?
   • A hyperbola has two branches that open in opposite directions, while a circle is a closed curve.
8. What practical applications do hyperbolas have?
   • They are used in physics, engineering, and navigation.
9. What is the significance of the foci in a hyperbola?
   • The foci are two fixed points used to define and construct the hyperbola.
10. What is the starting point of an Archimedean spiral called?

• The origin.

11. How are link mechanisms applied in machines?

• They create desired movements in engines, robotic arms, and manufacturing equipment.

12. Who was Archimedes?

• A Greek mathematician known for his contributions to geometry and mechanics.

13. Why do we use constant increments in constructing spirals?

• To ensure the spiral expands uniformly.

14. What is the role of a T-square in technical drawing?

• It is used to draw horizontal lines and ensure accuracy in drawing.

15. How can link mechanisms help in robotics?

• They can control the movement and functionality of robotic arms.

Presentation:

Step 1: The teacher revises the previous topic, discussing basic geometric shapes and their properties. Step 2: The teacher introduces the new topic, explaining different types of loci and their applications. Step 3: The teacher allows students to contribute by sharing their ideas on loci, and corrects them when necessary.

Teacher’s Activities:

• Explain the definitions and constructions of loci.
• Demonstrate the use of drawing instruments.
• Guide students in constructing loci.

Learners’ Activities:

• Participate in brainstorming sessions.
• Practice constructing various loci.
• Plot points on different link mechanisms.

Assessment:

Evaluation Questions:

1. Define an Archimedean spiral.
2. What are the practical applications of hyperbolas?
3. Describe a link mechanism.
4. How do you construct a hyperbola?
5. List the tools needed to draw an Archimedean spiral.
6. What is the difference between a hyperbola and a parabola?
7. Explain how link mechanisms are used in engines.
8. How can you use a French curve in technical drawing?
9. What is the role of the foci in a hyperbola?
10. Describe the process of constructing an Archimedean spiral.

Conclusion:

The teacher goes round to mark learners’ work, takes notes of learners who need help, and makes necessary corrections.