The adapter for a EOS body to a Canon FD manual is the adapter needed. The Canon AE1 uses the FD/FL lens mount. The one I purchased works without a hitch. Mine is a K&F Concept Pro lens mount for Canon FD, FL lenses. From a F1 to a 5D Mark 4 with no issue. 

FD-EOS fit for Canon FD mount lens and canon EF mount camera body. canon 60d is EF mount, so the adapter ring can work with your camera, but you need to check your lens mount. could you pls let us know your lens specific model? service(AT)kentfaith(DO NOT)com, Please note: It is not same between Canon FD mount and EF mount, this adapter ring is only for Canon FD mount lens, please contact us if you want to purchase for Canon EF mount lens. 

Please note: our M42 adapter ring could not be suitable for Pentax Takumar Super Takumar Carl Zeiss M42 series（aperture pin does not fully depress, small tabs sticking out), as ours depresses the aperture pin all the way down

 

HI your fujinon m42 55mm 1.8 and a sigma-z m42 135mm 2.8 are M42 mount, the item can fit your camera and lens 

Yes the FD-NEX adapter is what you need. I also have a a6000 and a Canon FD 50mm , 28mm, and a 300mm and they all work well with this adapter.