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Radius of curvature of an offset circle

  1. Nov 11, 2008 #1
    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?
  2. jcsd

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