Today’s guest blogger is Laura Overdeck, founder of Bedtime Math and former FIRST® coach! Like many FIRST supporters, Laura is passionate about advancing STEM education, and the mission of Bedtime Math is to help kids love numbers so they can handle math in real life.
Robotics might be one of the best blends of “left brain” and “right brain.” The coding behind the scenes is a fantastic display of logic: the order of steps, the number of times they should loop, the decisions the machine has to make as it follows instructions. Alongside that, we have all the beauty of spatial relations, as the engineer makes the different parts fit together to follow those instructions.
What we don’t think about as often is the math behind it all – the pure numbers driving those arms, wheels and gears. That may be because we often ignore the math behind many aspects of our daily lives. When we turn a gift box this way and that to use the least wrapping paper, we’re doing math without realizing it. When we stagger the start times to cook different parts of a meal, we’re doing math. Every object we handle has a size, a weight, a midpoint, and so on. All of that math comes into play in robotics, and the more deeply kids dig into those numbers, the faster they can build a robot that will succeed.
Take levers. When we connect two beams to make a spinning X, the motion will depend a lot on which holes you pick to peg them together. In fact, which hole is the middle one? Mindstorms beams conveniently have an odd number of holes, so there’s always an exact middle one. Then if you connect multiple beams in a straight line, what’s the longest beam you can make? It depends on how many holes overlap. The fewer overlapping holes, the longer your beam – but the more you overlap, the stronger it will be.
Then there are gears. When a big gear turns a smaller gear the smaller gear makes more than one turn for each turn of the bigger one. But how many more turns? It depends on the ratio of the number of teeth. A 40-tooth gear will make a 20-tooth gear turn twice around each time it spins once. But it will turn an 8-tooth gear a full 5 times. If you’re feeling brave and put other big gears on that little one’s axle and have that big gear turn some other small gear, you can multiply your leverage over and over.
This ties right into one of the most important math traits of a robot, and in fact any car, truck or other rolling vehicle: the turning radius. The farther apart the front wheels from the back, the wider the turn. And of course, the farther apart the left and right wheels, the wider the turn. Then we always ends up asking, when the robot makes one full turn, how many degrees do the wheels turn? That depends on the wheels’ width – their diameter, a favorite word from geometry class. When a roboticist can calculate that relationship between the degrees a wheel turns and the degrees the robot turns, all of a sudden a lot of other tasks become easier.
Beyond this, there’s a lot of math just in figuring out what your robot should do during the competition. In FIRST® LEGO® League, for example, the robot has to tackle a range of challenges, which take different amounts of time and skill, and which score different numbers of points. What’s the best combination of challenges for the robot to do? Which ones should the robot skip? When teams wrangle with their robot’s time required on each challenge and its success rates, there’s a lot of complex math happening.
We may wish that machines could do everything for us. Sometimes it seems like they already do. But when robots are being built by people, the people who know the most math will win!
On December 22nd, FIRST and Bedtime Math will be introducing a shared Pinterest board, where we’ll share fun, math-based content. In the meantime, be sure to follow FIRST and Bedtime Math on Pinterest!