I bought the tractor in January 1999 after I stumbled across an ad for it in a heavy-equipment sales newspaper, and paid $6200 to buy it and have it hauled 280 miles to my dad's farm.  It's a 1965 model, serial number T111R068427R.   The serial number breaks down as follows:

The 3020, covered with ice and waiting to be shipped from the seller's house in Indiana to my dad's farm.  It was mighty cold to be shopping for tractors that day, but the timeless grace and power of this design warmed me right up. See also:  Buying Tractors in Small Indiana Towns

In August 1999 I managed to get several hours in with the brushhog, and the tractor loved to work--after an hour in the field it ran flawlessly, much more smoothly than in all the times of driving around with kids in the wagon or some other no-load kind of play.  And my son and I replaced the burned-out oil-pressure warning lamp, which was a project in itself--even on a tractor built in 1965, metal housings get rusted together and demand patience and determination as payment for allowing themselves to be opened up without being destroyed in the process. 

In August 1999 I got back to the farm and adjusted the shifter linkages successfully, or almost succesfully, and all the gears worked--although then sometimes 3rd gear seemed tricky to find.

In August 2000, I took the tractor to the John Deere dealer to replace leaking oil seals on the load control shaft, and to replace the top shaft in the transmission since it still wouldn't shift very well.  And I realized that I don't get to use the tractor very often, and it's a pretty expensive piece of machinery to just let it sit around and get dusty and in the way... sigh.
 

Before trying to adjust the shifting linkage, I studied the 3010/3020 service manual to see if I could figure out what specifically might be wrong.  At the very least, I think I figured out how the Syncro-Range transmission itself works, and it's a lot simpler than I'd expected.  It consists of three parallel, horizontal shafts, each with gears on them:  The transmission shaft, which brings power directly in from the engine crankshaft, through the transmission clutch on the center of the flywheel.  It has three gears on it, one each for low range, high range, and reverse. The differential shaft, which takes power out of the transmission and passes it on to the differential.  It has four gears which correspond to the four shifting stations on the gear shift lever console:  one for 1st, 3rd, or slow reverse (depending on which range gear on the transmission shaft is used); one for 2nd, 5th, or fast reverse; one for 4th or 7th; and one for 6th or 8th. The countershaft, which has gears on it that mesh with those on the transmission shaft and those on the differential shaft, so power is transmitted from one to the other. The gears on the countershaft are all permanently fixed to the shaft, so the entire thing always rotates as a unit.  Shifting gears on the tractor doesn't physically change anything on the countershaft. The gears on the differential shaft are free to spin independently, except when one of them is engaged by shifting the tractor into gear.   In between each pair of gears is a smaller drive gear, permanently splined to the differential shaft.  Each drive gear is covered by a shifting collar, which is moved horizontally along the shaft by moving the gearshift lever.   The shifting collar has teeth on its inside circumference that mesh with the drive gear, and with teeth on the sides of the four transmission gears.  When the shifting collar is moved against the 1st/3rd gear, for example, its inner teeth are meshed with the drive gear and the 1st/3rd gear.  In that case the 2nd/5th, 4th/7th, and 6th/8th gears are not meshed with a shifting collar, so they still spin freely.  Changing the position of the shifting collars means physically meshing the teeth in the collar with those on the transmission gear, so it can only be done when the clutch is in and the transmission is not in motion. The gears on the transmission shaft are also free to spin independently except when one of them is engaged by shifting the tractor into gear.  But unlike the differential shaft, the transmission shaft does not use shifting collars with teeth that must be physically meshed.  Instead, it uses "synchronizers", these little clutch-like things that are mounted in between the range gears.  When you shift within a given station, you're not physically meshing any gear teeth--which is why it can be done when the tractor is in motion.  Instead, you're physically moving the synchronizer clutches--which changes which one of the range gears is actually driven by the transmission shaft and which ones are disengaged from it.  With the shifter lever pushed forward, towards the front of the tractor, the forward synchronizer clutch engages with the low-range gear, so the tractor is in the lower gear for that particular shifting station.  The high-range gear and the reverse range gear are disengaged and rotate freely.  When you pull the shifter lever straight back towards you, the forward synchronizer simply pulls away from the low-range gear and gradually engages with the high-range gear--so the tractor speeds up.  The teeth of the low range gear are still meshed with the corresponding gear on the countershaft, but the low-range gear is no longer driven--it just sits there and spins freely while the high-range gear is driven.  Since there's no meshing or unmeshing of teeth, you can shift back and forth between low range and high range without stopping the tractor.  When you move the shifter lever over to the right and then all the way back towards you, the forward synchronizer goes to a neutral position, and both the low-range and high-range gears are disengaged from the transmission shaft.  At the same time, the reverse synchronizer gets pushed against the reverse range gear, so then the tractor is in reverse.  The service manual is very well illustrated, and studying it has been a great education.  Call John Deere Distribution Services at (800) 522-7448 to order manuals for any John Deere tractor or piece of equipment.

The 3020 came out in 1964 as an upgrade of the 3010, which along with the 4010 was one of the original "New Generation Tractors" that John Deere introduced in 1960.  Although 3020s incorporated some significant improvements, the majority of features that made the New Generation tractors so versatile and capable were in all in place in 1960.  If you're looking for a tractor to use often with a front loader, a late 3020 with the Powershift transmission and the hydraulic controls on the side console by the seat would be a great choice.  For most other applications, there's not much you can do with a 3020 that you can't with a 3010.  Here are some of the major differences between the models (all information pertains to row-crop tractors; standards and utility tractors may vary a little bit):