I will also suggest the Little Machine Shop (LMS) 7350 deluxe lathe. It can do 3/4 pass through spindle work, and LMS also sells a "spider" for the lathe to support the back side of the rod stock which is passed through the chuck and spindle. I have had mine a couple years now and it has worked rather well. I like the fact it comes from the factory with a rotary DRO for most of the important axis (except for travel towards and away from the chuck). The motor has surprising torque for a 500 Watt motor, more than I expected.
LMS has a wide variety of upgrade parts available for their lathes, to include an extended saddle to gain the ability to machine an additional inch in diameter. They sell multiple chuck styles and sizes (I have the included 3 jaw chuck, and bought the optional 4 jaw chuck for it as well). The seller also has an all-metal gear-set available (which was purchased along with the spider). You are getting a source which stocks some good options and spare parts for their products, which is an additional value to me. The chuck-side is a #3 Morse Taper, and the Tailstock is a #2 Morse taper. There is even a tapered bearing set for the headstock available, which many people like.
I view this as the king of the 7 inch by X family of lathes. This model has a 16 inch bed, as versus the standard 10/12/14 inch bed. This gives room to use longer tailstock drills and accessories.
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