(Venki Ramachandran)




Suppose we start with a circle with center P. Let A be a point on the circumference. At time t=0, let the point A be on the origin O (0,0). At time t, the circle would have moved forward such that, the co-ordinates of A are (x,y) and the co-ordinates of B are (m,n).

Now in time t, the point A would have described a distance = R theta along the circumference. This is also the horizontal distance moved by the center of the circle P.

This horizontal distance moved by the center will be from Origin to the point Q = x + AB =

This gives us or

Considering the Vertical distance, Y = PQ-PB =

Thus we have


We also know that the circle would be moving with a constant angular velocity, W. Where theta = Wt.

Thus the equations can be represented as

x = R Wt - R Sin (Wt)
y = R - R Cos(Wt)



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