A circle of radius, R is made to rotate about a known offset distance,e from its center. Now the polar equation for the profile will be e-e*cos(theta)+constant, with theta the angle from reference. As I understand, the radius of curvature of this curve should be a constant R. Surprisingly, when I use the polar rad. of curv. eqn. I get a varying radius of curvature instead of constant, R. For example, if R=2 and e=1. This will give r(@) eqn as 1+(1-1*cos (@)) I get rad. of curvature varying (cyclic)from approx. 1.8 to 2 instead of constant 2. Why the rad. of curvature should vary for a circle, eventhough it is rotated about offset center? Is it true for offset circle that at any time the osculating circle at any point should be the circle of radius,R ? If it is true, why the polar curvature formula is not working here?