SummaryOne of the rules when filleting is the radius used can not run off the edge of the surface it is following. In the case of tangent cylinders, one surface edge is going to taper down to a zero width at the tangent point. This tutorial show how to build the fillet surfaces manually.

Tangent cylinders

Download Rhino 3DM file

Original tangent cylinders.

Filletedge - Take what Rhino gives you as a starting point - You can also FilletSrf.

Extend the upper cylinder down a little (White surface). FilletSrf between this and the lower fillet surface - the result is the red surface. Use Extend=No.

Note the red fillets peter out just before they hit the tangent point.

Turn on points and SetPt the last points in the fillets to the midpoint between them along the edge of the lower blue fillet. Zoom in close to the tips of the arrows at step 3 to see the result.

Trim using the edges of the fillets and join up.

Make sure to delete any unjoinable stray bits of fillets left after trimming.