In the 1980's, Maytag top-load washing machines had two drive belts underneath the machine, one driving the water pump and one driving the drum and agitator through a transmission.  These are commonly referred to as "2-belt models", and after Whirlpool bought out Maytag they were sold under both names.

The transmission works as follows:  When the motor is turning the pulley clockwise (as viewed from the bottom), the brake is released and the entire transmission and drum start rotating, eventually very rapidly for the spin cycle.  When the motor is turning the pulley counterclockwise, the brake remains engaged and the transmission and drum remain stationary while the transmission converts the motor's spinning into an oscillation motion for the agitator.  Meanwhile, the water pump also gets rotated both directions; Counterclockwise it just foams up the soapy water inside its plastic housing, but clockwise it pumps the water from the tub out through the drain hose.

The early transmission type is now referred to as the "helical" or "Newton" transmission, and it's a big clunky-lookin' thing with a massive counterbalance:

Maytag helical transmission

This was superceded by the simpler, more compact "orbital" transmission, part number AP4373301 or 6-2097750:

Maytag Whirlpool orbital

Early versions of the orbital transmission had 8 bolts on that cover, but evidently somebody figured out that 4 would do the job.

The helical transmission went out of production and is no longer available; you can't buy parts for it other than the gasket.  However, there are so many laying around in shops and junkyards that people have found ways to keep them working.

Measuring from one end to the other, these transmissions measure 23 inches.  Note that there are similar transmissions -- orbital, anyway -- that measure 25" end to end but otherwise appear virtually identical; the shaft and spline are just sticking farther out the bottom end.

If you have a helical transmission that has gone bad, you can buy an orbital transmission to replace it.  It will fit perfectly and work fine.

AGITATION:  In agitation mode, the center agitator in a top-loading washing machine turns back and forth.  There are those who put great stock in how far it turns back and forth, with 180 degrees (a half a turn) seeming to be the break point; those that turn farther than 180 degrees supposedly clean clothes better than those that make shorter oscillations.  Speed Queen, maker of arguably the best washing machines on the market today, proudly advertises that their agitator turns 210 degrees.  If you buy this argument, you will want to know that the Maytag helical transmission will turn the agitator a bit more than 180 degrees; I didn't measure it, but it looks like perhaps 190 degrees or so.  The orbital transmission, on the other hand, turns the agitator considerably less than 180 degrees, perhaps 100 or 110 degrees or so.  Yeah, barely more than a quarter turn.

The orbital transmission will also agitate faster.  Good or bad?  My wife and I opened the lid and jammed the safety button and watched the agitation from the orbital, and it looked OK to us.  It seems to generate an interesting rollover of the clothes, moving toward the center and then downward along the agitator, presumably because the agitator is pushing the water and clothes outward at the bottom.

PLASTIC GEARS:  Both the helical and the orbital transmissions look like massive blocks of metal from the outside.  However, the two gears inside the orbital transmission are plastic.  The gears inside the helical transmission (there are several) are metal except for the bottom pinion which is plastic.  Plastic gears may or may not be a sign of poor quality, as in some applications plastic gears will actually last longer than metal gears.  Hopefully, either transmission would last a good long time.  The failure modes on the helical transmissions seem to primarily involve the oil leaking out rather than gear failure -- although lack of oil might obviously lead to gear failure.

OIL:  There are reports online that people opening up their 30-year-old transmissions are finding the oil a thick, goopy mess.  If you have such a transmission and you intend to keep using it for a while, you might want to drain that old oil out and replace it with a modern gear oil, or at least fresh Maytag gear oil.  Unfortunately, there's no obvious way to drain and refill this transmission; it looks like you'd have to get it out of the washer and then split it in half.  Ugh.

There is an easy way to drain and refill an orbital transmission:  Remove the front panel from the washer, lay the washer on its back, and roll the drum around until the cover on the transmission is facing straight up.  Remove the 4 (or 8) screws and remove the cover.  Then, while holding a can or something under it, roll the drum to one side and pour the oil out.  Roll it back to facing up, pour in some fresh oil
; with the cover off, the orbital case should be within a half inch or so of full.  Apply some sealant and reinstall the cover.  If you have an orbital transmission that's getting up in years, this might be a good way to maximize its longevity.

SEAL REPLACEMENT:  Occasionally one of these transmissions gets incontinent and dumps all its oil out the bottom.  The pulley and belts then sling it all over everything under there, the belts start slipping, it's a real mess.  Time to buy a new washer and dryer set?  Well, if you're that kinda person, perhaps.  But if it's an orbital transmission, it almost certainly can be fixed pretty easily.  There's a YouTube video showing how to remove a rubber cap and a small screw, pop off a drive key, then spin the big pulley off the bottom.  You'll be looking at the lip seal which is pressed into the bottom of the transmission.  There's supposedly a $90 tool for removing the seal, but the video shows how to grind the tip of an old butter knife into a suitable tool for prying it out.  The replacement seal kit, AP4024008, includes a plastic tool for installing the new seal.

Maytag transmission seal kit

Tap it in, remove the tool, and put the pulley and drive key back on leaving about 1/2" of free play between the pulley and the drive key.  Then you'll want to top up the oil using the method described above.  You'll probably also want to replace the drive belts; you'll never get all that oil off of them.

If you have a helical transmission, you're not so lucky.  The lip seal that can be replaced was only introduced in June of 1986.  If your transmission was built later than that, you can replace the lip seal using that seal kit -- but you'll still be faced with figuring out how to top up the oil level inside the transmission.  If your transmission was built earlier than that, this seal kit will not work for you -- there's no place in the transmission to install it!  Where the later transmissions have a black rubber lip seal, the earlier helical transmissions have a bronze bushing, as shown in this photo:

Maytag helical transmission
          bottom end

The seal on these older transmissions is part number 2-10286, and it's up inside the case, not down on the bottom where you can get at it.  What's more 2-10286 is a fancy part number for an O-ring.  Any engineer worth his salt knows an O-ring should never be used as a running seal, they should only be used to seal stationary plugs and connections, but the guys designing this gearbox didn't get that memo until June 1986.  As a result, sad to say, if your gearbox is leaking oil out the bottom, chances are only too good that it's the earlier type with the sorry O-ring seal.  Since the transmission would have to come out and apart to replace that O-ring, you need to consider whether to tackle that job, or just install a new orbital style transmission instead (with the later design lip seal), or just buy a new washer and dryer set.

AGITATOR SHAFT TREATMENT:  If you're rebuilding or otherwise reusing one of these transmissions, you might want to address corrosion issues on the agitator shaft.  This shaft is immersed in the laundry water with every load.  Over a coupla decades, it's probable it'd end up looking pretty bad.  The new orbital transmission in the photo above has an agitator shaft that is jet black, presumably due to a coating that hopefully will help protect it.  The old helical transmission in the photo above looks like bare steel; if it was ever coated, the coating has worn away.  If you tear it apart and sandblast all the parts, you'll take the old coating off.

So what can you do to protect your agitator shaft?  One rebuilder online mixed up JB Weld 2-part epoxy, thinned it with water, and painted the shaft with it.  Good plan, I suppose, but what I would use would be POR-15.  In 20 years, that coating would still look like new!

You don't need to take the tranny apart to coat the agitator shaft.  The coating only needs to extend through the seal on the drum support, which is some distance above the transmission housing.  You can just mask the housing and coat the portion protruding, and the seal will run on the coating and everything in the water will be fully coated.

EXTRANEOUS O-RINGS:  One online site shows an O-ring being installed in the groove at the very top of the transmission where the agitator shaft emerges, and another shows an O-ring being installed on the agitator shaft itself just below the agitator splines.  Both are shown in this photo, although the rubber thing under the splines looks like a rubber collar rather than an O-ring:

Extraneous O-rings

I have no idea what either rubber ring is intended to accomplish; they're not sealing anything.  I assembled my washing machine without either one.

LUBRICATION DURING ASSEMBLY:  In watching numerous YouTube videos and replacing a transmission myself, I was struck by the lack of indications of using any lubricants when putting a washing machine together.  If you're tackling this job, I recommend the following:

If you remove and replace the brake assembly for any reason, anti-seize compound should be applied to the threads prior to installation.  Anti-seize compound should also be applied to the threads of that little screw that holds the locking device that digs into the threads on the brake.

On a couple of places online, it is recommended that about one tablespoon of oil be poured into a new brake assembly to prevent it from squealing when stopping.  I concur that a tablespoon of something should be poured into it, but I would recommend automatic transmission fluid (ATF) rather than oil.  ATF is formulated for brakes, bands, and clutches, whereas oil will just reduce the brake's effectiveness.  There are two types of ATF, Type F and Dexron; either one should work.  Whatever you pour in is not likely to ever come out; the brake package is shaped in such a way that fluids won't pour out even if you tip it.

Before dropping your transmission into place in the tub support in the washer, I recommend applying Extreme Pressure (EP) Molybdenum/graphite grease to the splines, both on the transmission and inside the brake assembly.  Don't goop it on too thick; you don't want it flying off and getting inside the brake.  Use a toothbrush to apply just a thin coating, and wipe off any excess.

There are "damper pads" under the tub support that it rocks around on.  If you have to lubricate them for any reason, the EP grease would probably be a good choice.

Before setting the tub down onto the main tub bearing on top of the transmission, I recommend the outside of the metal sleeve that's slid onto the transmission and the inside of the bushing in the bottom of the tub be lubricated with wheel bearing grease.

Before installing the rubber boot over the spigot in the bottom of the tub, I recommend lubing up the bottom end of the rubber boot with plumber's grease.  NOTE:  Take care not to get any on the other end of that rubber boot, the end with the mating face for the running seal.  I did find mention of using dishwashing liquid here instead of plumber's grease, but the person making that suggestion also mentioned having a dickens of a time installing that boot.  One other installer suggested using spit, but I doubt if that will help installation much either.  Using plumber's grease, I had no trouble at all installing it.

Before installing the drum support, which screws onto the top of the transmission, the portion of the agitator shaft that contacts the rubber seal in the center of the drum support should be lubed with plumber's grease, along with the inside of the seal itself.  Again, make very sure nothing gets on the running seal face which is the larger diameter ring on the underside of the drum support.  That running seal needs to be assembled dry, and in fact the face on top of the boot and the face on the bottom of the drum support should be wiped with a dry cloth just prior to installing the drum support to make sure they are both clean and dry.

Also before installing the drum support, the threads should be lubricated with anti-seize compound.  Again, only a light coat; you don't want globs of it in there.

After the drum support is on, wipe away any excess plumber's grease before dropping the drum in place.  Anything left in here ends up in the laundry; plumber's grease is pretty innocuous (safe for drinking water), but you still don't want it in your laundry.

You should apply anti-seize compound to the threads on the setscrew in the drum support; remove the setscrew entirely, apply anti-seize compound with a toothbrush, and screw it back in.

I recommend applying anti-seize compound to the threads on top of the drum support prior to installing the drum nut.

After installing the drum nut, wipe away any excess anti-seize compound lest it end up in your first load of laundry.  That stuff will stain clothes big time.

On the older machines with metal tubs, the metal tub cover is installed with a big rubber seal with a triangular cross-section and a two-piece band clamp; the clamp has two tightening screws 180 degrees apart.  The seal should be installed dry against the tub cover, but it'd be a good idea to apply some plumber's grease to the inside surface of the clamp itself.  This will allow the clamp to slide easily around the seal and tighten uniformly.
  If either the tub or the tub cover are too rusty to seal properly, it is recommended that the rusty area be sanded smooth and recoated with POR-15.

I also recommend the threads on the clamp screws be lubed with anti-seize compound.  This clamp needs to be very tight to ensure this joint doesn't leak when the tub is full of water.  The screws should be located in corners of the cabinet; if on the front and back or sides, they may bang against the cabinet when loads are out of balance.

I didn't find any instructions or videos on how to reinstall that tub cover, so I'll provide a couple of tips.  Assemble the tub cover, gasket, and clamp loosely so that you are able to pull the tub cover up or push it down.  Note that the "fin" needs to be to the rear; that's what contacts the out-of-balance shutoff switch.  Close the top of the cabinet and install the two screws that hold it down.  Looking into the top of the machine, rock the tub around until the center of the tub cover aligns with the center of the cabinet opening.  Peering through the open front of the machine, observe the clearance between tub cover and cabinet top.  It should around 1/4" to 3/8", and it should be the same all around.  Pry areas up or press down as required.  Once properly positioned, tighten down the band clamp.  Rock the tub around to make sure it doesn't hit the cabinet.

Anti-seize compound, ATF, EP grease, and wheel bearing grease can be found at any auto parts store.  Plumber's grease can be found anyplace that sells plumbing supplies, including Lowe's or Home Depot.