I want to build a 'bot as a prototyping platform, and one of my requirements is encoders on the drivetrain. Excluding the computer, what are cheap ways of building something that meets that requirement?
We typically build a 6 wheel drop center drive, so I’d like something that comes close to replicating that.
I have custom sheet metal available as an option, but would be OK with buying something as a starting point.
Unless you can get donated frames or machining, I think the cheapest way to make a drive base is to buy a 2016 KOP from Andymark (http://www.andymark.com/AM14U3-p/am-14u3.htm), especially when they come on sale infrequently, and US Digital encoders for the toughboxes (http://www.andymark.com/E4T-OEM-Miniature-Optical-Encoder-Kit-p/am-3132.htm)
One option I haven’t looked at before is using FTC parts.
For example, I could use four of these NeveRest motors and four of the inexpensive Omni wheels.
That would run me $60/wheel all in. Any cheaper options?
Anyone have any experience with these N20 motors with integrated encoders?
I could potentially use the inexpensive Vex Omni wheels at $10/each with those.
How about your robot from last year? That would be free, and very quick. 
FIRST CHOICE also has encoders, and those would be sort of free. Whatever’s fastest and cheapest is probably parts you already have. What do you have on hand?
I’d like something that a) can be put in a car by one person and b) doesn’t require leaving the car out of the garage.
Do you want cheap, or do you want cheap cheap?
When we did AndyMark Fight Night, I pulled two NeveRest 40s out of our failed-testing pile, stuffed a little churro on them (slice it an inch or so along the axis, wiggle a screwdriver, jam it on the NeveRest shaft), and then found a couple 1/2" hex Performance Wheels in our scratch and dent pile (which could easily be swapped for the far-cheaper Stealth Wheels). Even if you had to add a couple Collar Clamps to the churro to make sure it stayed engaged with the NeveRest (I didn’t with the aluminum Performance Wheel), you’re still under $40 a wheel.
How you handle the other side is an open question; I just let the chassis drag along the warehouse floor with some clear packing tape as a slider block. Some casters from the hardware store would certainly get you started until you wanted more.
Cheap Chassis - total cost ~200 (with 4 motors)
REV Hex motors (that include encoder cables) http://www.revrobotics.com/rev-41-1301/
60 mm wheels (no hub required) - http://www.revrobotics.com/rev-for-ftc/motion/wheels-hubs-adapters/wheels/
Extrusion - 2-3 pieces depending on how big a chassis you want http://www.revrobotics.com/15mm-extrusion/
Motor mounts - http://www.revrobotics.com/rev-41-1027b/
corner gussets - http://www.revrobotics.com/rev-41-1305/
shaft collars - http://www.revrobotics.com/rev-41-1327/
Hardware - http://www.revrobotics.com/rev-41-1361/ & http://www.revrobotics.com/rev-41-1359/
Do you want repeatable cheap or coincidental cheap?
I got a bunch of AndyMark ToughBoxes from MicroCenter on triple discount - that’s coincidental cheap.
I got a bunch of Grayhill encoders cheap from a surplus shop - that’s coincidental cheap.
Then there is cutting corners on the frame cost and just slapping on some inexpensive motors.
You certainly can scale down a FRC style robot. I have a test frame I fit into a largest hard shell suitcase you can carry on a plane. You put the battery, laptop, and charger elsewhere. It fits in the back of my 2005 Honda Insight Hybrid Coupe over the electric motor and batteries (the car is considered sub-mini) and as that back is a hatch I can lift it out myself (I am a 6’3" 280lbs male and the case has swivel wheels with retractable handle, which came from Walmart).
Stacked plate drive train can be made with a simple drill press and Forstner bits with some care. Stack them with spacers made of pipe or whatever you’ve got handy. Use cheap threaded rod and some Loctite to save some cash on hardware. Worst case for wheel hubs pour some Shapelock/Polymorph in the hub and mold to need, locate center with a jig or lawnmower blade balancer before you start. If you have a Tractor Supply nearby they usually carry cheap bearings. Should be able to cut the aluminum plate to shape on a table saw and/or a miter saw. Could even do this with wood: just remember that wood changes dimension with the seasons (and lesser grades of plywood have voids inside the layers) so use a decent grade of plywood or even aircraft rated wood. Might look at steel tubing in the auto part store for the spacers.