# Engineering a Solution to a Closet Mishap

### A true story about gravity, math, and how 3D scanning and 3D printing saved the day

If it weren’t for the fact that my wife had been out of the house running errands for a few hours I would have thought she was in on another home improvement project scheme.
It all started when our oldest son was moving out of the house.

After years of poking holes in the drywall of his bedroom, we asked him to do some spackling for repair. He had some wall-mounted speakers that had wires running through the wall and into the attic. The only access to the attic was through our bedroom closet, so he went up there to remove them.
I was downstairs at the time when I heard this loud THUD from upstairs.
I ran upstairs only to find my son at 9.8 m/s² had fallen through the access and was on the floor. Thankfully, regardless of his acceleration due to gravity, he was okay—our closet, not so good.

We had one of those wire-rack things that went around the perimeter of the closet, and it all came down. All I could do was to make sure he was okay and then walk out of the room shaking my head.

When my wife came home I took her upstairs to show her the carnage. She walked into the closet, said, “Oh my!” Then she turned around with a wide smile and firmly proclaimed “We’re getting new closets!”

After a few trips to the “save more, do more” store we had purchased some of those modular do-it-yourself (DIY) units where you can configure your own layout. While installing the units we came to a spot in the closet where the wall was angled.

This was a spot where we wanted to put a rod across to hang clothes, but the bracket was square and didn’t accommodate for the angle. With no special tools to measure the angle, I had to reacquaint myself with a little trigonometry. I remembered there was a way to find all the angles of a triangle if all three sides were known.

With a little help from the Internet, I was reintroduced to the SSS law of cosines.

I drew a 2-inch horizontal line on one wall, another 2-inch line on the other, and then measured between them to get the third side. With this information, I found 2 of the angles, and for the last angle, I subtracted the first two from 180° to get the third angle.
It looked something like this (show your work!):

COS A = (b² + c² – a²)/ 2bc
COS A = (2² + 3.75² – 2²)/ (2 x 2 x 3.75)
COS A = (4² + 14.0625² – 4²)/ 15
COS A = .9375 The angle is the inverse, so A = COS¯1 .9375
Angle A = 20.36°
Angle B was the same as A, so to find C = 180 – 20.36 -20.36
Angle C =139.28°

### Reverse Engineering

Armed with this information I had the angle that I needed to reverse engineer the new angled bracket. I used a 3D laser scanner to scan the existing bracket. Using Geomagic Design X, the scan gave me the overall shape and hole locations so the new one would mount up correctly.

Once I had the design finished, I used a Stratasys FDM 3D printer to print out the new brackets in ASA white plastic. I had to mirror the bracket for the other side of the rod (something I found out during install – DOH!).
All in all, we turned a misfortunate event into a fun project and now we have a new, well-organized closet. I’m happy, but more importantly, my wife’s happy!