_____ GeometricaIContructions 4.51
Special Curves
- Construct a cycloid having a rolling circle of 60 mm diameter. Also draw a tangent and
normal at any point P on the curve. - A circle of 40 mm diameter rolls along a straight line without slipping. Draw the curve traced
by a point on the circumference, for (a) one complete revolution and (b) one and a half
revolutions of the circle. Name the curve. Draw a normal and tangent to the curve at a point
25 mm from the straight line. - A circular wheel of diameter 100 mm rolls over a straight surface without slipping. Draw the
curve traced by a point P for one revolution of the wheel. Assume that the critical position of
the point P is at the top of the vertical centre line of the wheel. Name the curve. - Draw an epicycloid having a generating circle of diameter 75mm and a directing curve of
radius 200 mm. Also draw a normal and a tangent at a point P on the curve. - Draw a hypocycloid for a rolling circle of diameter 75 mm and a base circle of 250 mm
diameter. Draw a tangent and a normal at any point on the curve. - Draw an involutes of a hexagon 000 mm side.
- The evolute of a curve is a circle of diameter 30mm. Trace the curve.
- Draw the curve traced out by the end of a straight line 308 mm long as it rolls over the
circumference of a circle 98 mm diameter. - Draw the involute of an isosceles triangle of sides 20 mm, and the other side 15 mm for one
turn. - Draw the involute of a semicircle of radius 25 mm.