I started with the image and then using an inscribed circle of 10
Started building the triangles, circles and tangent points then trimming.

seems the lobe circle is a factor of 1.5 and then slid back to a second triangle tip point.
using the intersection point a circle can be created to a tangent point then trimmed.

now to figure out how to work backwards from the needed lobe size.
or you can always scale the item to suit once drawn.

My way of proof of concept and grasping the idea

now to figure out how to work backwards from the needed lobe size.

I knew someone was watching me THAT was my next question !
I fiddled with it last evening a bit but gave up early.

The other issue is where to place the center of rotation to produce a given "throw".
https://en.wikipedia.org/wiki/Reuleaux_triangle

Thanks 

If you know the fork width (2), and the desired corner radius,
wouldn't the base triangle just be the fork width minus 2 x the corner radius ?
 

Now, make the throw 1.

After I posted, went back and found I ASSumed some things and I was visually close, but mathematically wrong. 
wish id have seen that webpage before i posted
will have to go back and re-address.
thanks for the link
another good brain teaser to fend off dementia 

pretty cool functional device, it did remind me of the Wankel engine

I'm no trig'er, but it looks like everything could be worked out from a few right triangles.

GIVEN:
Fork width   = 2
Corner rad  = .2
Complete throw of the fork = 1 (.5 x 2)

 

 
Simpler than I initially thought.

Thank Ya folks,
 

Arts Gearotic might help?

http://gearotic.com/

Maybe Art could add this to his assortment of "Gearotic Gizmos" 

Still did not follow all that last image but it gave me some ideas.
once i understood the tangent points i could create a circle from three points
then the light bulb came on and it all made sense
thanks again
Proves how we can not see the obvious sometimes. yep pretty simple.

will have to pass the info off to Art and see if someday he can fit it in. He does stay busy coding.

Id forgot to post this image of two different ones
changed only the tip radius

I knew you could do it