I'm afraid that's not a problem that can be solved, it being the nature of anything open-ended drawn with any non-continuous linetype to "fill out the ends," beyond full cycles of the linetype definition, with continuous extensions [in closed objects, it can make adjustments].  You can minimize them by adjusting the length of an object [when that's not made impractical or impossible by other considerations], but you can't get rid of them entirely.

For some reason I couldn't get it to work using typical Unicode "\U+0xA3" format as a text element in a linetype definition, as I had hoped, but that turns out to be the British Pound sign in most fonts.  I see that waynelem didn't say whether the rings alone are what's wanted as John's image shows.  The following worked pretty well for me, to make one with line segments between the rings but not across them, but that can be changed.  It requires that you have a Text Style defined in the drawing that is called WINGDINGS and uses the WINGDINGS font.  At a linetype scale of 1, the rings are 1 unit in outside diameter, and the spacing is 4 units C-C.  [For your 36" ring size, use it at a linetype scale of 36; the C-C spacing will be 144.]  It's pretty precise, but you can fine-tune those decimals if you want it even more so.  For a different spacing, divide the desired C-C spacing [when the rings are 1 unit in diameter] in half, subtract 0.5, and use the result in place of the 1.5 entries at the ends.

 

*WHATEVER,whatchamacallit ----o-----o-----o----
A,1.5,-.5,["ÂŁ",WINGDINGS,x=-.616,y=-.4987,s=1.083],-.5,1.5