Great idea, just needed to be a little taller on my bike. My wife's backrest is good where it's at, bolting two hinges together worked.
If you'll notice in the 2nd and third pictures, they are slightly pulled apart, showing how much more length I believe I needed. In my opinion, there wouldn't be enough support and the hardware would bend. So, before I even started, I decided on more rigidity and a radical change to my original design. Am I happy with it? An awesome "Yes!"
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Step 1: I'd Mentioned Placing a 3/16 Plate Between the Hinges, 'til I Found This in My Stash
I had the fortunate choice between these two square tubes. The thought occurs to me as I type these words, since these tubes fit inside each other, I could have made a telescoping adjustment instead of what I did. I don't regret it though. I got to do way more crazy cutting and welding, something I like to do anyway. I also wanted to see if I could do what I envisioned.
I chose the inner square tubing, the smaller one. Let's take a look at it, what will it look like, before I weld it. How long do I make it? I chose to make it a little longer, worse case I would have to cut some of the length off the top, rather than have to weld another 1 1/2 on top. Can be done, don't want to spend my time doing it here.
Step 2: Since I Was Hasty in Painting This Thing Every Time I Thought I Was Done
I got to clean the paint off every time I was done. Wire brush on my grinder worked awesome in removing the paint. Did not work awesome at removing the chrome finish on the tubing. I switched to my sanding disc for this.
I marked where I needed to cut out the section of the hinge. When I placed the tubing, I wanted it to be flush with the surface of the hinge from the backrest.
Step 3: This Is What I Call, "Using the Force"
What it's able to look like before you weld it. Welding in tight spaces that you'll have to undo is more like making scrap for the future. You may not be able to "go back". I try not to have to undo welding if I can help it.
Step 4: I Could Have Created a Space for My Adjustment Bolt Later, I Cut This Early
At the last second, I saw it to be easier in creating this space for my allen wrench with my cutting wheel. Did I make it far enough, no. When I use a 1/2 drill to make it longer it will be. It was less work to cut this notch before I started welding.
Metal moves when it heats and cools. Tacking, or spot welding several places can make the difference of having to cut out welds because your work moved so much while welding from one end to the other. I probably made 10 tacks before I started really joined the tubing to the other part. It worked great, there was almost no warping at all. Nothing the adjustment bolt couldn't take care of.
I did give it a careful twist with a crescent wrench after I finished this project and had it placed on the bike. It was off maybe 5 degrees. Fortunately working with iron you can bend and twist it sometimes.
Step 5: Ah, That Feeling of It Being Able to Adjust to the Right Place.
I didn't have a drill press, that would have been able to drill straight through both sides accurately. So I measured down both sides of the tubing from a half inch for the first hole, then 3/4 of an inch, and drilled each side.