Looks like an 86 660. If the rims are Saturae and Mavic, they've probably both been replaced at one point or another. IIRC those had Matrix (Trek house brand) rims.

Freewheel and shifters may be recent changes. Bike was originally 6-speed.

Not sure what to tell you about the crank. I remember Trek's 600EX kit for 86 included Specialized cranks (144 bcd), BB, pedals, hubs, headset, stem, and bars (made, respectively, by Sugino, Sugino, MKS, Sanshin, I forget, Nitto, and Nitto).

Frame should be 531 throughout, although that may be a Tange fork.

Hope this helps

Mel