What is hypocycloid and epicycloid?

is that epicycloid is (geometry) the locus of a point on the circumference of a circle that rolls without slipping on the circumference of another circle while hypocycloid is (geometry) the locus of a point on the circumference of a circle that rolls without slipping inside the circumference of another circle.

What does the word hypocycloid mean?

Definition of hypocycloid : a curve traced by a point on the circumference of a circle rolling internally on the circumference of a fixed circle.

What is hypocycloid in engineering drawing?

A hypocycloid is defined as the locus of a point on the circumference of a circle which rolls without slip around the inside of another circle.

What is the equation of hypocycloid?

-cusped hypocycloid is produced, as illustrated above (Madachy 1979). is the angle between the radius vector and the tangent to the curve….Hypocycloid.

	hypocycloid
4	astroid

What is the equation of Hypocycloid?

What is the difference between epicycloid and cycloid?

is that epicycloid is (geometry) the locus of a point on the circumference of a circle that rolls without slipping on the circumference of another circle while cycloid is (geometry) the locus of a point on the circumference of a circle that rolls without slipping on a fixed straight line.

What does a hypocycloid look like?

In geometry, a hypocycloid is a special plane curve generated by the trace of a fixed point on a small circle that rolls within a larger circle. As the radius of the larger circle is increased, the hypocycloid becomes more like the cycloid created by rolling a circle on a line.

How are epicycloids constructed?

Epicycloids can also be constructed by beginning with the diameter of a circle and offsetting one end by a series of steps of equal arc length along the circumference while at the same time offsetting the other end along the circumference by steps times as large.

How do you derive the equation of an epicycloid?

For the case of an epicycloid you can derive the equation in a similar way. You should get something like: the minus sign in the second term of the equation of the x coordinate is due to the fact that the rotation of the rolling circle and the motion of its center are in the same direction.

How do you find the parametric equation for a hypocycloid?

If the initial configuration is such that P is at ( a, 0), find parametric equations for the curve traced by P, using angle t from the positive x -axis to the center B of the moving circle. The resulting curve is called a hypocycloid.

What is the polar angle from the center of an epicycloid?

The polar angle from the center is To get cusps in the epicycloid, , because then rotations of bring the point on the edge back to its starting position. An epicycloid with one cusp is called a cardioid, one with two cusps is called a nephroid, and one with five cusps is called a ranunculoid .