Lesson Notes By Weeks and Term - Senior Secondary 2

LOCI, ARCHIMEDEAN SPIRAL, HELIX, HYPERBOLA AND LINK MECHANISMS

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TERM – 1ST TERM

WEEK TWO - FOUR

Class: Senior Secondary School 2

Age: 16 years

Duration: 40 minutes of 5 periods each

Date:

Subject: Technical Drawing

Topic: LOCI, ARCHIMEDEAN SPIRAL, HELIX, HYPERBOLA AND LINK MECHANISMS.

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

I.)  Construct an Archimedean Spiral                         

II.) Construct a hyperbola 

III.) Construct a Links Mechanism

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 discusses the importance of archimedean spiral, hyperbola and Link mechanism.

Students listens attentively to the teacher                                                                         

STEP 2

EXPLANATION

Teacher guide students to construct archimedean spiral, hyperbola and Link mechanism.

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

LOCI, ARCHIMEDEAN SPIRAL, HELIX, HYPERBOLA AND LINK MECHANISMS.

The Locus of a Point

The locus of a point is the pattern or line produced, when the different locations of a moving point are joined together from its starting location to the last location. Locus of a point is used in different fields such as in mathematics, physics and chemistry to plot graphs; or, in engineering such as in fluid mechanics, thermodynamics, and machine design to analyze a selected system meant to be studied.

In Technical drawing, we will use it develop certain models or tools or the things that engineers use to produce machine parts or to analyze the machine part. Examples of some of the things we would be developing are involute, Archimedean spiral, parabola, hyperbola, ellipse, etc; and we shall state the uses of each of these things we will construct.

Construction of an Archimedean Spiral

An Archimedean spiral is a type of spiral that increases in radius at a constant rate. In technical drawing, it's often used for various applications such as representing spring coils, certain types of screw threads, or as a design element in architectural plans or mechanical engineering drawings.

Procedure

  1. Draw a vertical and horizontal line
  2. Mark the point O, the shortest radii OA and the longest radii OB
  3. With O as the centre and a radius OB, draw a circle and divide it into 8 equal parts.
  4. Divide AB into the same number of the equal parts.
  5. With O as the centre and radius O1, draw an arc to cut the radial line from 1.
  6. Repeat the same for 2, 3, 4, 5, 6, 7 and 8. Draw the curve through the points to obtain the curve

 

Construction of hyperbola

The Hyperbola is the locus of a point that moves so that the ratio of it's distances from it's Focus and Directrix (eccentricity) is constant and is greater than unity (>1).

Lines which is tangent to the hyperbola at infinity are called asymptotes.

To construct a hyperbola when given a foci and a transverse axis.

  1. Draw a straight line Q-Q of any convenient length and locate the position of the given foci F and F1 and the transverse axis VV1 on it
  2. From the focal point, mark off any convenient number of equal unit to the right to get point A, B, C, D, E etc
  3. With F1 as centre and radius VA, draw an arc above and below the transverse axis. Then with F as the centre and radius V1A, draw arc to cut the previous ones as shown above.
  4. Repeat the procedure for B, C, D and E. Join the points of intersection to obtain the curve.

 

Construction of a Links Mechanism

In a link mechanism, a member called the crank has a connecting rod attached to it by a pon joint. As the crank rotates  through one revolution, the connecting rod is therefore made to move in a specified direction.  A point on the connecting rod traces out a path as the crank rotates. The mechanism is drawn in several positions and the new position of the point marked. The principle of link mechanism makes it possible to determine the forces present in a mechanic system.

To construct a Link mechanism:

  1. Draw a circle to represent the movement of the crank, if it is to rotate through one revolution.
  2. Locate the initial position of the crank and connecting rod and construct them just exactly the way they appear on the given question having studied the dimensions
  3. Identfy the direction of the movement of the crank,(In the case below, Clockwise), which implies that crank will move frome the starting point A, to 1, 2, 3....and back to A, While the connecting rod will experiences a corresponding linear displacement along the centre line.
  4. The position O on the connecting rod to each position of the crank's rotation is marked. I e P1 for A 1 and so on

EVALUATION: 1. The figure below shows a link mechanism. Crank OA revolves clockwise about O, while link AB slides through the block C. Draw the locus of the point pon the link mechanism for one revolution of OA. (WAEC)

CLASSWORK: As in evaluation

CONCLUSION: The teacher commends the students positively