Urgent help needed: point on a circle transformation

[xguardianx]

I'm faced with the following math problem in my program:

There is a point on the circle. The circle is moving to right by X amount only in horizontal direction. At the same time, the point is rotating counter-clockwise by "alpha" radians.

When the circle has moved by X amount, what is the new location of this point on the circle?

Obviously, both its position in x, y has changed. How do you find the location of the new point?

Any help is appreciated and its very urgent ;-)

PS: The radius is known.

 

[galactus]

When the wheel rolls a certain distance, the radial line form the center to

the point P on the perimeter rotates through an angle \(\displaystyle {\alpha}\).


We need to express P(x,y) in terms of the angle alpha. The coordinates of the center(C(h,k)) and the point(P(x,y)) are related by:

\(\displaystyle x=h-r\sin{\alpha}\) and \(\displaystyle y=k-r\cos{\alpha}\)

Since the height of the center is the radius, we have \(\displaystyle k=r\);

Since the distance h moved by the center is the same as the arc length

subtended by \(\displaystyle {\alpha}\), we have \(\displaystyle h=r{\alpha}\)

So, we have parametric equations:

\(\displaystyle x=r{\alpha}{-}r\sin{\alpha}\) and \(\displaystyle y=r{-}r\cos{\alpha}\)

Is this what you needed?. This gives the coordinates of the point knowing the radius and the angle rotated through.