Completed vise

Chamfer cut in the front. This is helpful when sawing things like half blind dovetails

simple handles. Parts of these came from my old vise, but these are simple to make

Materials

I recommend using hardwood, but many people have made a Moxon with softwoods and like them. I have 4/4 oak. It was labeled as white oak (good) but turned out to be red oak (bad) oh well
24" of 3/4" allthread. Yes, acme thread is better. No, I don't think it's much better in this specific application
Six (6) 3/4" nuts
Two (2) 3/4" ID washers

Two (2) 3/4" ID (1" OD) sleeves
The hardware costs about 20.00. 

I'm going to try to stick to basic hand tools for this build, but due to some drill bit size limitations, I did need to use my forstner bits in a drill press. I'm not going to focus too much on rough lumber prep. If you are interested, this is how I do it

I start breaking down the rough sawn oak to manageable lengths. I am building a 22" wide, 5 1/8" tall vise. This is personal preference based on how I work. Consider the widest pieces you'll be putting in the vise and make sure you have room between the two screws. Most plans call for a 36" long vise, but for me that's too cumbersome. Especially considering this needs to be stored  between uses.
I need 3 pieces. 1 for the movable chop, and 2 (laminated) for the fixed chop

After broken down, I plane them down. I would have planed them in larger sections, but this wood had some twist. Cutting them down to size eliminated most of the twist, making this part much easier and allowing me to retain some thickness. 

The only plane I used is a Stanley No5. Thickness doens't matter, but try to leave everything as thick as possible

I choose the pieces that I'll laminate and the orientation

Then I turn my attention to the edges. 

Note the movable chop is taller. This is intentional and will help position the vise on the bench for use

Getting ready to glue the pieces. I used a decent amount of glue because this is a lot of material.

Something something too many clamps. I leave this for almost 24 hours. That's a lot of surface to stick together.

Now is a good time to saw that piece of threaded rod in half.

I'm scraping the squeeze out before I plane it. Dried glue is tough on plane soles and irons. 

Planing it flush after getting the glue off. This is why I love the jack plane. It does rough and fine very well. And this is my "rough" plane 

This complicated mess of arrows illustrates what I am doing now. I am intentionally bowing the inside of the movable chop. This is an important step with a thinner (or softwood) chop. The bow creates a huge mechanical advantage.
The taper is easy. Lay out the board in quarters. Plane from the edge to the first line until that line is gone. 
Now plane from the edge to the center line until it's gone. 
By doing so I am taking 2 passes from the first quarter of the board, but only one pass from the second quarter of the board

Do the same on the other side. If tear out is an issue, plane from the marked line toward the edge.

Here you can see the progress. I make pencil lines across the whole board and plane until it's gone. I did the first quarter here. It's important the board's face stays square to the edges, so check/adjust that as well. 

End result. With a flat board on top, you can see there is a bow in the chop. It takes extra effort to close the vise, but all that clamping power is concentrated in the center (where the work piece is). Try to get this gap the same on both sides

Now time for drilling.  I mark out where I want the rods. 3" from the edge and in the center of the board. I mark it with an awl

IMPORTANT Remember the movable chop is taller. Be sure you are measuring from the top of the board, and use the thickness calculated from the rear chop. In this example, my rear chop is 5 1/8". So I measure 2 9/16" from the top edge. 

I Use a very small diameter drill bit and drill through the piece. Use whatever you have that drills holes. I used an egg beater drill but a drill press would be ideal It's very important this is straight. 

Measure the nut you got. This is about 1/18"

On the rear of the fixed chop, I lay out the 1 1/8" hole for the nut

I drill it just a little shy of the depth of the nut (represented by the caliper here). I am going to double-nut this so the rod will not spin. I used a drill press here because I don't have an auger bit that size. 

This is why I drilled a pilot hole. From the other side, I drill all the way through with a 3/4" bit for the rod.

Here is the result

Now I need to chop a mortise for the nut. I put the rod in the 3/4" hole and spin the nut on. If I didn't get the holes dead centered, this will account for the error and keep the rod centered at least. 

I chop out the recess. This doesn't need to be super clean. make it so the nut fits in fairly tight. There will be some epoxy in there

Nut fits in the mortise. I had to tap it in gently. I make sure the floor of the mortise is clean so the nut isn't crooked. that will cause issues. 

Now for the movable chop. I measure the sleeve. This allows the chop to slide easily while still maintaining a tight tolerance (no elongated hole needed) The package says an inch, but I' want to be sure. I drill 1" holes all the way through.

Sleeve epoxied in. I had to hammer this in so no worries about clamps. I only used epoxy here because oak grows and shrinks a lot with seasonal expansion. In another more stable species, a compression fit would have been fine. Scuff the sides before applying the epoxy. 

Here I test it out without handles, It fits and the chop slides super easy. If not, the rods may not be coming though completely straight. The one consequence of using the sleeves is the tolerance is tight and there is little room for error. The chop will bind if the rods aren't straight. 

I'm happy so I epoxy the nuts in and clamp them. Be careful not to get any on the threads

This piece of cherry will be attached to the back. It will help stabilize the vise and give me a place to hold it down with holdfasts

I applied glue and am putting in a few screws as well. Pre-drilling is a must in oak. The screws act as clamps so I don't need to let this sit around while the glue dries. 

Everything fits

Final test with the handles. The handles are made just like the rear chop. 1 1/8" hole, half the nut exposed, and a through hole. I added cranks on the bottom that I turned on a lathe. They spin freely around the bolt and are attached via a threaded insert. 

Now I plane the top flush

Clamping test. This piece of zebrawood isn't coming out at all. The vise moves smoothly and does not rack top-to-bottom

Here I lay out for a chamfer. While not necessary, I like to mark lines. It keeps it clean. A chamfer here gives extra clearance for when a cut needs to be made with the saw on an angle - half blind dovetails for example

There are lots of ways to do this. I see a lot of people do stop cuts. a series of saw cuts to both lines then chiseling out the waste. I prefer this shinto rasp. I was done in about 5 minutes - including sanding

Done. Ready for final smoothing and finish

Now to smooth out the chop one last time. Make sure those sleeves are below the surface. If not, sand it. I then applied a finish - Boiled linseed oil and shellac. 

2 things left to do once the finish dries. The first is to determine the maximum amount of rod I want sticking out of the front. This will limit how far the vise can open. Once I do that, I will put my last 2 nuts n the back and lock them down with a wrench. This will prevent the rods from spinning. If I ever want more or less capacity, I can loosen the nuts and adjust the rod

The other is to affix some leather to the movable chop. That's it!