I've been using fully adjust monitor arms for a number of years, but they are heavy, and I realized that I never actually adjust them. I decided replace them with something fixed, and this was the solution that I came up with.
The total cost for these monitor arms was about $40, including the glue and all of the screws needed to mount them.
Step 1: Parts
The base of the mount is made of two parts. A flange, and an adapter. The flange is actually for a 3" or 4 " pipe (there were no 2" flanges available), and the adapter goes from 3" to 2".
I also bought some slip connectors so that I could cover the hole from the top, and create a stronger mount. This isn't entirely necessary, and could be left out, especially for smaller monitors.
Step 2: Planning
This adds additional complexity to the design, since the holes must be drilled in exactly the right location, or the monitors won't be located correctly.
This also meant that I had to contend with the frame of the desk, and make adjustments to the location to accommodate the cross member.
This aspect of the design can be changed quite easily so that the flange can be mounted on the top of the desk (as explained in the next step).
The pictures below are of the completed mounts.
Step 3: Assembly
Since this is backward from the way that the flange is designed to mount, it's fairly stiff, and takes quite a bit of work to get it inserted. Since it was so snug, I decided not to disassemble and glue the joint, but if it was mounted the other direction, I would probably glue it.
I then cut and drilled short pieces of PVC pipe for test fitting the mount.
Step 4: Monitor Adapters.
I ripped a piece of plywood at 5" wide, and then cut 3 squares just under 5".
Then I temporarily attached the old mount with screws to use as a guide.
Once I had drilled the 4 mounting holes, I then drilled the center hole, and hammered a long bolt through the hole.
Step 5: Drilling the Desktop, and Test Fitting.
I then made adjustments to the measurements, and drilled the actual desktop.
The two extra holes in the desktop are for the cable grommets.
Step 6: Mounting the Flanges
I glued a 2.5" piece of pipe into the flange, and then screwed the flange to the bottom of the desk. Then glued the straight connector to the top of the pipe, sandwiching the desk between the two pieces. This design is permanent, and required that the holes be very exact in order for the monitors to line up.
Once mounted, I reattached the PVC test pipes to the monitors to get a final measurement for the pipe sections that would hold the monitors.
Step 7: Finish
I got the center monitor done first, carefully measuring to get it level, and parallel to the desk. After allowing it to dry, I did each side, making minor adjustments to both the height, and angle of the pipe during the gluing process.
As an added bonus, the pipes are large enough to run the cables through them, so there's no exposed monitor cables on the desktop.
I'm very happy with this design; It's very rigid, and feels like it will hold up for a long time. The frame under the desk is height adjustable, and there is no shaking or movement from the monitors while raising and lowering the desk.