# Lesson Notes By Weeks and Term - Senior Secondary 1

Special curves II

TERM – 3RD TERM

WEEK TWO

Class: Senior Secondary School 1

Age: 15 years

Duration: 40 minutes of 5 periods each

Date:

Subject: Technical Drawing

Topic: SPECIAL CURVES II

SPECIFIC OBJECTIVES: At the end of the lesson, pupils should be able to

I.) Construct a Cycloids

INSTRUCTIONAL TECHNIQUES: Identification, explanation, questions and answers, demonstration, videos from source

INSTRUCTIONAL MATERIALS: Videos, loud speaker, textbook, pictures,

INSTRUCTIONAL PROCEDURES

PERIOD 1-2

 PRESENTATION TEACHER’S ACTIVITY STUDENT’S ACTIVITY STEP 1 INTRODUCTION The teacher explains the meaning of Cycloids and its applications. Students listens attentively to the teacher STEP 2 EXPLANATION Teacher guide students to construct Cycloids Students exhibit attentiveness and active engagement STEP 3 NOTE TAKING The teacher writes a summarized note on the board The students copy the note in their books

NOTE

SPECIAL CURVES II

Cycloid

A cycloid is a curve traced by a point on the circumference of a circle as the circle rolls along a straight line. It is defined as the locus of a point on the rim of a rolling circle. Cycloids have unique properties, such as constant curvature and length of arc.

It can also be referred to as a curve generated by a point on the circumference of a circle which rolls in a plan surface along a straight line without slipping.

Applications of Cycloids

1. Cycloids model the paths of projectiles launched horizontally or at an angle under the influence of gravity.
2. Cycloids are used in the design of gears, where the shape of teeth ensures smooth and efficient motion transmission.
3. Cycloidal gears are employed in mechanical clocks and watches for accurate timekeeping.

Construction of Cycloids

1. Draw a circle with a given diameter.

2. Divide the circle into 12 equal parts, numbering each part.

3. Draw a line equal to the circumference, that is, πD and divide the line into 12 equal parts as well.

4. Draw a line from the diameter of the circle through the line in 3 above.

5. Draw a horizontal line from point 1 as shown below

6. Locate the point such that the line drawn is equal to the radius of the circle.

7. Match the points such that the line drawn is equal to the radius of the circle, for instance, 2 on the circle matches with 10 on the horizontal line as shown below.

8. Repeat the process for 3, 4, 5 and 6. Join the points together as shown below.

9. Complete the curve as shown with mirror image already draw. Hence the required Cycloid.

EVALUATION: 1. Construct a locus of a point P on the circumference of a circle diameter 60 rolling along a straight line without slipping. Construct a tangent and a normal to the locus of a point from the right end of the locus.

CLASSWORK: As in evaluation

CONCLUSION: The teacher commends the students positively