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I have a problem with a sphere rolling on a fixed sphere. My problem is to find relationship between coordinate of center of sphere (X,Y,Z) and orientations (alpha, beta, gamma) or Euler angles of sphere. as we know a sphere has 6 DOF in space (3 coordiantes and 3 rotation) when a sphere rolling on surface we expect that it have 3 dof beacuse of relation beween coordinate and rotation.

for example when a circle roll on a surface the x coordinate of its center is:

X=R*teta (R = radius of circle) and it has one DOF.

Like the circle rolling i want to find the relations for sphere.

thanks

hossein