First things first….. let’s sort out the spread of bits in those photos.
Put to one side for their cleaning and lubricating in sets:
Chucks and faceplates – these are the work-holders that screw onto spindle, the hollow (presumably) shaft right through the headstock. There are two chucks there, at front right, plus what seem three faceplates; the discs in the middle with various holes and slots (for clamping work-pieces not readily gripped in the chuck.)
The gears. Those with keyways and stamped or embossed numbers (their tooth-counts) will be the “change-wheels” for screw-cutting and fine longitudinal feeds. They are used by setting appropriate combinations of them on the spindle and leadscrew (the one right along the lathe’s length), so somewhere among all the bits should be an intermediate plate with a long slot in it, called the “banjo” from the usual shape of them. I can’t see it on the bench so it might be in its place on the lathe, below the outer end of the headstock.
There may be four gears that seem not to match the general pattern of the change-wheels. See if they form two pinion/gear combinations with the same total number of teeth on both, say (40 + 65), (30+75) for sake of example. They might be for a “back-gear” giving a two-stage extra low spindle speed – I use that on my lathe when screw-cutting, and machining irregular objects. I cannot determine if your lathe has this, but if it does they form an arrangement with two on the spindle and two on a parallel shaft behind the headstock, with locking / engaging means. A clue may be the presence of machined seatings and tapped screw-holes on the back of the headstock.
Having cleared the decks for action a bit…
The big arrangement to the right is the saddle / cross-slide / top-slide assembly. It has some way to allow linking it to the lead-screw, involving that block already on the screw. The block has dropped round so facing the wrong way. The general shapes and the sizes and alignments of screw holes should show where things meet; but I cannot say if there is something else betwixt block and saddle. Usually there is a hefty casting there, called the “apron”.
The lever is for engaging and disengaging the half-nut(s) by which the saddle is driven along the bed by the screw, from the spindle via the change-wheels.
Dave’s photo of a Myford lathe shows the usual pattern, but if this is a slant-bed lathe as Dave H suggests, that block om the leadscrew may bolt straight to somewhere on the saddle.
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That’s the primary parts but there is an intriguing collection of components left…..
The object immediately in front of the lathe, to right of the half-nut block, seems to be a milling-spindle, a useful accessory (it needs its own drive via that pulley on its end) but not part of the machine itself.
The four small blocks with hefty screws and hook-like protrusions, by the faceplates, may be “faceplate dogs” – for clamping work to the faceplate via the slots. Also there are what appear the chuck-keys: square ends and Tee-handles.
Below the name-plate: the small item is possibly a stub-axle for holding an intermediate gear in the change-wheel train? The shaft, apparently, with a nut on the end, might be part of the back gear IF fitted?
I can’t identify the:
– Elegant trilobe thingummy.
– Three rod-based components in the middle,
– The casting between the tailstock and the large faceplate. It might be an accessory not part of the machine; perhaps related to the putative milling-spindle.
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Finally, as this was made in Canada, will the various screw-threads be of BSW or BSF, or American (UNC / UNF) form? Replacements for both may be obtainable though not necessarily to the right length. The UN ones would be easier to find; and the hexagons are to the (a/b)” A/F nomenclature.
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Hope this helps!