Calculations and Math in Engineering Notebooks?

I’ve been looking to see how I can improve my team’s notebook for next year. I’ve read many of the other threads here regarding tips on engineering notebook. I’ve seen many of the same things: follow the rubric, CAD, PID, use a lot of pictures, be consistent with the format, etc.

However, there was on aspect that really interested me that many people have suggested (and something I’ve been suggested multiple times in my time in robotics): use calculations and math in your notebook. I know it impresses a lot of the judges and makes you stand out. This is definitely something I want to start doing, but I’ve never done calculations in my notebook and I haven’t been completely sure on how you could use calculations in the notebook and how teams have utilized them.

In this thread I want to hear about some of the use of calculations in robotics and how they can be used in future seasons. I’d also like to hear some examples of math teams have done in their notebook that really impressed judges and the usefulness of it.


Mechanical advantage could be a head turner

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Pretty much anything that makes you stand out, and shows that you have put real thought into your robot. Math, calculations, gearing, ect.

When we were designing our lift we calculated the theoretical lifting times and capacities for different gear ratios given motor torque and power.
We also calculated loads/torques on chains and gears and other mechanisms and compared these to their breaking strength as well as some trig for lift banding and some other stuff.


Depending on how advanced your programmer is, they will have boatloads of math lying around.


I’m not sure about this year, but I know that a lot of teams wrote down their projectile math for their various ball launching devices during turning point. Basically any math that you use for your robot can be written down


I coach middle school IQ but there are 2 simple examples I used with them. They later admitted it helped show them how math is practical

  1. I made them measure the diameter of their wheels and from there get to number of rotations for the motor to move their robot X distance. I wouldn’t let them use distance in Vex blocks until they demonstrated it this way.

  2. they had a rack and pinion type lift and used some simple math to figure out number of motor rotations to lift a cube just high enough to clear all the pins as they drove across the field


It really depends on the game. Like in turning point and nothing but net you could do a lot with projectiles and if you used sensors you can try and do odometry which would loom pretty impressive. Then like this year in tower takeover my team did a lot with gear ratios, torque, lbf, center of gravity, voltage, current, etc . All that math was really helpful because we would know how much we would need a gear ratio to be to hold a certain amount of cubes and our tray at different points of the tray being lifted. The math we did relating to the motors was also really helpful and can be used for any game. We also did a lot of speed calculations for the drive base and certain lifts based on different weights. Also if you have any math in your programs you should be able to show math in the notebook for that like in PID loops.


Did you then compare to actual lifting times and capacities. I’d be interested in seeing that comparison.


This year I calculated all of the torque and speed values for different sprocket sizes on the rollers to find which one we needed. I also created a custom ranking stat that factors in WP, TRSP, and OPR (It was more representative than CCWM this year)


We were planning to but never got around to doing it in the end

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Any calculations applicable to the design/implementation of your robot should go in the notebook. Also, judges really like to see that.

In addition to some of the things listed in this thread, I did some basic math on the physics of the tilter (ie. force x radius x sin (angle) = torque, math for torque and rpm of the motors) and the arms. Then, I compared it to the torque of the cubes and arm/tray metal to show the judges that it would work theoretically as well as experimentally.

Remember to relate whatever you do math for to back to what you are trying to demonstrate by doing the math, such as a justification for a change on leverage, banding, lift capacity, or efficiency of a component.


I agree with a lot of what’s been said here. A lot of people have given some really good examples of places in which you can start incorporating some more math and physics into your design process such as gear ratios, calculations of mechanical advantage, etc.

Of course, it is great to know specific places to use physics to reinforce your design process, but please don’t get the idea that using physics is a “box to check off on the rubric.” The biggest reason using physics helps with your notebook is that it shows a high level of thought and a high-level reasoning involved in your design. As such, I encourage you to, rather than simply do some calculations of the obvious places where physics applies, think of physics as your primary reasoning for making decisions. Within my team, we have a lot of ideas, and a lot of these ideas are often based on intuition or simply feelings that things may work. Of course, our intuition about these things has improved a lot in the last 5 years, but it helps my team a lot to make sure that we can justify ANY decision we make with physics, from gear ratios to tray angles to even our autonomous motion profiling. Essentially, the point I’m trying to make is that thinking about mechanics and design from the more theoretical math/physics standpoint is extremely helpful and something you should try to do throughout all your decisions, rather than just for your notebook.


This is similar to what @Aditya_Narayanan said, but I think being here at the beginning of the season is a great place to begin implementing math into your engineering notebook as a way for planning, and especially not just using complex math.

If you can show that you had a certain set of specifications that you wanted your bot to fit instead of just basic functionalities (a very basic example: we designed our bot to have a 9 second cycle time, made up of a 2 second descore, 4 second intake and movement, 3 second score) , and then you can show how either you fit those parameters or if those parameters changed and why, that will show a great bit of discipline on your team’s part.

Even if you have plans for designs already, you can acknowledge that the designs came before the calculations and then explain what you learned by crossrefrencing your designes and your math (e.g. we originally wanted our intake like this, and while it would have gotten the job done, it didn’t meet our standards and we decided to keep looking)

(Also I know that I’m using the cycle time analysis as a baseline example, but there are many other places where you could do something similar to this)

It’s important to think about how the math doesn’t need to be complex physics and algebra, it can be something as simple as a timing chart


So I am my team’s notebooker, and we actually got Excellence at every single comp we went to this season without any calculations or math whatsoever. I think that it is a great idea and you should definitely use a lot of numbers in it.

Something I’ve noticed over the past two years is that notebooks seem to look more like diarys than engineering notebooks. And I understand that an engineering notebook is a diary, but the ones I’ve seen seem more personal almost. If you’ve ever looked up what an actual engineering book should look like, they’re very detailed and descriptive instead of a paragraph of “Today we…”

So I guess what you should do is take a look at some professional engineering books and see what methods they use to convey what they did and how they did it. Using math and calculations is very important and those suggestions were correct. Good luck this season, I hope you’re good at tic tac toe!


So I guess what you should do is take a look at some professional engineering books and see what methods they use to convey what they did and how they did it

Do you (or anyone else) know of any way to access any professional engineering notebooks?
That would definitely be a good resource to include in this conversation.

Honestly I do not. I have looked up some google images of a couple, but they are really simple. I’m not sure if you could access any but I bet if you looked up engineering notebooks for a specific field (like “Engineering design for White House”) you might get better results.