A circle of 50 mm diameter rolls on the circumference of another circle of 150 mm diameter and outside it. Trace the locus of a point on the circumference of the rolling circle for one complete revolution. Name the curve.
Answers
Answer:
circle of 50 mm diameter rolls on the circumference of another circle of 150 mm diameter and outside it. Trace the locus of a point on the circumference of the rolling circle for one complete revolution. Name the curve.
Given:
Diameter of rolling circle Φ = 50 mm
To Find:
The locus of a point on the circumference of the rolling circle for one complete revolution.
Solution:
1) Draw a circle with a diameter of 50 mm.
2) Mark the circle's centre with the letter C then draw the horizontal and vertical axes.
3) As indicated in fig. 3, divide the circle into 12 equal sections and label each section 1, 2, 3, ....12
4) Starting at point P on the contact surface of the circle and the ground, draw a straight horizontal line of length D.
5) Split the line into 12 equal pieces, counting 1', 2', 3', etc (same no. as that of the circle).
6) Redraw a circle of 50 mm in diameter with the centre at "D distance.".
7) Create vertical lines from points 1, 2, 3, and 4, and then label them C1, C2, C3, and C12, correspondingly.
10) Draw a horizontal line through a point on the circle close to point P, using C1 as the centre and a radius of 25 mm (the radius of a rolling circle). That is a P1 point.
11) Continue with the same steps up to C12 and record points accordingly through P12.
12)Draw a straight line that passes through all 12 points (P1, P2,..., P12), then give the curve a name.
13) 35 mm away from the horizontal line, mark a point M on the curve.
14) Cut the horizontal axis at point Q and mark it using M as the centre and a radius of 25 mm (the radius of a rolling circle).
15) Draw the horizontal line perpendicular to Q and label it N.
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