Don’t all kids love trig?
I was always pretty good at math. The first math class that really got me excited was trigonometry. To me it seemed really useful. Ok, so that’s not normal – but there were plenty of times in my young life that I wanted to calculate something trig could have solved. Maybe it was figuring out how long a 2×4 needed to be if I was going to strengthen one of the makeshift forts we built using scrap lumber, or how long the plywood needed to be for a bike ramp. Didn’t all kids need this stuff?
So once I got to engineering school, naturally statics class felt the same way. For the non engineers, statics is one of the most basic mechanical engineering disciplines for figuring out forces in stationary structures. In a nutshell, if it isn’t moving, then all forces sum up to zero – cause if they didn’t – things would start moving. Moving stuff is the domain of dynamics, not statics. Statics uses tons of trig to figure out stuff like “if you push on this thing at this angle, what’s the downward component of the force.” In statics you learn how to draw something called a free-body diagram. You use the diagram to see what equations will all sum to zero but will allow solving for the component force you need. Statics was a bit intuitive for me so I often found myself helping classmates with their homework.
See it Better First
Time and again while helping someone figure out their statics, I would start with the diagram. Students would begin with a tiny, poorly scrawled, out of scale sketch of the problem. Sometimes the diagram was too small to really help get an intuitive sense of the problem. I’d almost always start with a clean sheet of paper and say “draw it bigger and neater, then let’s talk about your equations.” So often a good clear drawing that was a bit more to scale made it obvious if you had used sine or cosine incorrectly in the equation. You could just tell from the drawing that the force you were looking for was wrong and you should double check your trig.
This methodology works for much more than statics. The essence of “draw it bigger” is this: if you’re having trouble solving your problem, draw it again clearer, or from a different angle. Literally look at your problem from a different perspective and get clarity.
Schematics – not just for electricity
Sometimes that different perspective is to draw the problem a bit more schematically. Mechanical engineers aren’t usually taught about schematics, those are usually reserved for electrical engineers. Electrical schematics are a drawn representation of an electrical circuit. Each line represents an electrical pathway. The schematic doesn’t get bogged down in WHAT the pathway is made from. It could be a trace on a printed circuit board (PCB), or it could be a thick copper wire. The schematic merely tells you what’s connected to what. If you’ve ever tried to fix an electrical problem, you know how hard it is to trace down the culprit. A schematic allows you to visualize the circuit even though you might be staring at a mess of wires, or the circuit might actually be connecting inside a PCB where you cannot see it.
The same thing works in the mechanical world as well as the electrical world. You can often simplify a mechanism or other mechanical system into a schematic that helps you see through to its essence. A mechanical schematic is like a stick figure version of a technical drawing. There aren’t clearly defined rules for mechanical schematics like there are for electrical schematics. Perhaps that’s why few use them, you might have to make it up as you go along.
Nothing Left to Take Away
My favorite engineering quote is from an early French aviator and author Antoine de Saint-Exupery “A designer knows he has achieved perfection not when there is nothing left to add, but when there is nothing left to take away.” The sentiment of that quote could be a topic unto itself, but the idea of stripping away the non-essentials is at the heart of using schematics and clearer drawings to solve a problem.
I’ve used mechanical schematics to figure out some complex cam follower geometry, especially rotary motion. Sometimes you can “unroll” the rotary motion and see it more clearly if you draw it linearly. Once you have it understood in the linear realm, you can roll it back up to rotary motion and still understand it.
There’s a time and place for highly detailed drawings that represent what your design really looks like. But when you’re trying to figure out a vexing problem, strip it down to it’s essence. Take away everything that’s not necessary. Look at your problem without all the extra geometry getting in the way. Draw it bigger, simpler, clearer, from another angle. Let the drawings inform your intuition. Once you work things out in schematic form, let the details back in.
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