formula nearly ellipse rotated next same shape remains in contact

[grehom]

Does anyone know the formula for the nearly elliptical shape, which when rotated next to same shape offset by 90 degrees remains in contact throughout its rotation through 360 degrees (and no I want something more elliptical than a circle). If you start with two ellipses one touching the other one at its major radius and the other at it's minor radius eg |-- and try to rotate both in same direction at same speed they start to collide. There's probably a special name for this shape but I can't remember ever hearing of it.

 

[Bob Brown MSEE]

google "oval gears"

http://www.youtube.com/watch?v=ZqNROIUjuv0

 

[grehom]

http://www.youtube.com/watch?v=ZqNROIUjuv0

Thanks for that, that's exactly the kind of shape I need - less the teeth. I want four near elliptical cams geared to all rotate at same speed to form as close to air tight seal as possible- it's basis of something called a 'Walley engine'. I'd like to try and build one. If I had the formula I could play with the shapes so I can get the compression ratio right. Thirty years since I did any mechanical engineering but this looks like fun project. Mind you, I suppose teeth might improve seal at cam faces!