A circle of 40 mm diameter rolls along a straight line without slipping. Draw the curve traced by a point on the circumference, for one complete revolution
Answers
Answer:
The curve you are referring is a Cycloid.
Cycloid is the curve traced by a point on the circumference of a circle as it rolls along a straight line.
When a circle of radius r rolls over a straight base along the positive direction of x-axis through the origin, then a point (x, y) on the circumference generates a cycloid above y axis (y ≥ 0). Parametric equation for t (angle by which the rolling circle rotates) is given by,
x= r(t-sin t) , y=r(1-cos t)
As the circle keeps rolling, series of cusps (called an arches of the cycloid) are traced. The first arch of the cycloid consists of points in the range 0 ≤ t ≤ 2 π
For given diameter 40, r= 20.
x= 20(t-sin t) , y=20(1-cos t).
PLEASE MARK BRAINLIEST
Given Data:- Diameter of rolling circle Φ = 50 mm
Normal and tangent point = 30 mm above straight line.
Assumption – Circle is rolling towards right side (Show the direction)
Procedure:-
1) Draw a circle of 50 mm diameter.
2) Draw horizontal and vertical axis and mark centre of the circle say C
3) Divide the circle into 12 equal parts and name each division 1, 2, 3, ….12 as per shown in fig.
4) Draw a straight horizontal line of length πD from point P at the contact surface of circle and ground . 5) Divide the line into 12 equal parts 1’, 2’, 3’…..12’ (same no. as that of circle).
6) Draw again a circle of 50 mm diameter at πD distance with centre C’.
7) Draw horizontal and vertical axis for 2nd circle.
8) Draw horizontal lines from points (1,11) (2,10) (3,9) (4,8) (5,7) and 6 up to vertical axis of 2nd circle .
9) Draw vertical lines from point 1’, 2’, 3’,…. 12’ up to horizontal axis and name it C1, C2, C3….C12 respectively.
10) Taking C1 as centre and 25 mm radius (radius of rolling circle) cut the horizontal line passing through point on the circle near point P. Mark that point P1.
11) Repeat the same procedure up to C12 and accordingly marks points up to P12.
12) Draw smooth curve passing through all 12 points (P1, P2, ….. P12) and name the curve.
13) Mark a point M on the curve at a distance of 30 mm from horizontal line.
14) Taking M as centre and 25 mm radius (radius of rolling circle) cut the horizontal axis and mark that point Q.
15) Draw perpendicular from Q on horizontal and mark it as N.
16) Draw a line passing through M and N (NMN is normal).
17) Draw a line perpendicular to normal from point M (TMT is required tangent)