Question 3
(a) Fig. 2 shows a circle with link OP attached to it. The circle rolls
along KS without slipping
(i) Plot the locus of the point O when the circle makes one
revolution.
(ii) name the curve produced.
(i) construct a square equal in area to the rectangle.
(ii) measure and state the length of the square
Observation
Candidates that attempted this question could not adequately plot the locus of the point, as specified. Most of them, however, were able to satisfactorily construct a square with similar area to that of a given rectangle.
The solution of the poorly answered part of the question is given below.
(a) PLOTTING THE LOCUS OF A POINT (P) ON A CIRCLE
FOR ONE REVOLUTION
MAJOR REQUIREMENTS FOR PLOTTING THE LOCUS SUPERIOR TROCHOID
- Drawing the base line KS
- Drawing the rolling circle R25 on the line KS
- Drawing the generating circle R 35 concentric to the rolling circle
- Dividing the concentric circles into 12 equal parts
- Laying out the circumference of the rolling circle on the base line
- Drawing vertical lines on the divisional points on the base line KS
- Drawing horizontal lines from the divisions on the generating circle to the vertical lines
- Using radius 35 and at different centres C1, C2, C3…. C12 and locating the points of the locus on the corresponding horizontal lines
- Joining the points into a smooth curve
- Name the curve – SUPERIOR TROCHOID
- Neatness and quality of linework