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Bookshelf Woodworking

Obelus and Radical

The Boy’s bedroom projects continue…

He has a lot of books, of course, and a newly modelled bedroom that didn’t offer anywhere to put them. I could’ve bought a regular, free-standing bookshelf… Alright, I couldn’t. I was bound to end up building one, wasn’t I?

His room had a thin slice of wall in the corner alongside the window. I could make something to fit in there. Having build the tumbling boxes bookshelf in our end room, I decided to use the same technique for his room; to create something a little abstract and irregular, but fitting for him. I should say at this point that he has a flair for Mathematics. In year 5 at primary school he was selected to take part in a county-wide, inter-schools maths challenge, and now attends maths symposia at his secondary school.

When you make shelves as random boxes, you begin to see patterns in them. As I was messing about with designs (in Powerpoint, naturally), one pattern I kept imagining was of mathematical symbols. I could picture shelves made of plus and minus signs, maybe a divide symbol (an Obelus, apparently) and other symbols to spot between the books. I had just made his desk out of maple, and the shelves in the end room were ‘oak’ (that is, poplar, stained to look like oak.) Perhaps I could pick out the symbols by making them out of the darker oak-effect, and used maple for the remainder of the shelves.

With the seeds of this idea, I went to work in PowerPoint. It took a few goes to figure out how big the symbols should be compared to the shelves as a whole. I measured a variety of his books to see what sort of sizes I needed to allow for, and I jiggled around the shapes until they fell into place. As the figure below shows, the symbols didn’t work if they were too big, and they fitted best when I spread them out more randomly and ensured plenty of lighter wood between them to give them contrast. I decided to go for the design on the right.

Off to the wood store with another order, this time for maple and poplar planks. There would be lots of them, many being quite small and fiddly. It took five pieces to make up the Obelus, three pieces each for the addition, multiplication and π (pi) symbols, but there was one shape in particular that would introduce new challenges.

Down in the bottom-left corner, I had decided to add a square-root symbol (a radical with a vinculum, I am informed.) This comprised three lines, two being sloped. I would need to saw at an angle, and work the biscuit cutter on a sloping section. But first I would need PowerPoint to help me plan out exactly what to cut.

I settled on having the long descending line at 15 degrees from vertical, and the rising tick at the end to be at 45 degrees. This would mean taking 15-degree strips off the ends of the two longer pieces and a 30-degree strip off the end of the shorter piece. Sawing could be achieved using a jigsaw with its base set to an appropriate slope. Handily, my jigsaw’s base is designed with neat slots that allow adjustments in 15-degree increments.

The figure below shows the cuts between the longer pieces. (Note: confusingly, this image is reversed, since I wanted to identify which piece was which and I had written labels on their backs, where they would eventually be hidden by the wall.)

More problematic was the positioning of the grooves for the biscuit joints. In particular, the top joint, between the two longer pieces. In a right-angled joint, the grooves are cut perpendicular to the faces that are glued together, so the sides of the grooves are parallel to the sides and end of the wood. In this case, the end and the inner side both slope in towards where a perpendicular groove would be. There was a risk that the grooves would cut through and weaken or damage one of the surfaces. I decided that the safest approach would be to cut the grooves so they would be parallel to these sloping sections. This is probably easier to understand from a sketch, so in the picture below, the biscuit would sit as shown in the lower figure rather than as in the upper figure.

The biscuit joiner would hence be set to cut at an angle to the faces to be glued. Tricky… I devised a jig that would hold the cutter at 15 degrees to the wood. I had to allow for the fact that the angle would result in the cutter not being flush with the surface of the wood at the point at which the blade appeared. So, I set the cutter blade to extend further out into the wood so that the resultant hole would still be deep enough. In the end I managed to get the two pieces to line up with the top one overhanging by about a millimetre. This was good – I could easily plane off the excess wood to create a smooth, flat join – better than if it had been a millimetre too short!

I shall talk about the assembly, and the problems that befell the mounting, in part 2.

Cheers

Nick

By nickcnickcnickc

I spend my working life staring at computer screens, so in my spare time I look for things to do with my hands, preferably involving wood. It's a little ironic then that I've now starting writing a blog about my woodworking, and thus introducing computer screens to my main hobby..!

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