Instructables
Picture of Understanding Motor and Gearbox Design
Why Spend Time Choosing the Right Motor and Gearbox?
Choosing the correct combination of a motor and a gearbox for a given application is very important, both in the FIRST Robotics Competition (FRC) and in actual engineering projects.  Without appropriate motor-gearbox combos, your team will find that your robot does not function as quickly and effectively as intended, and may have a tendency to burn out motors.

This tutorial will teach you the fundamentals of gearbox design and implementation.  First, I will teach you about motor characteristics.  Next, I will discuss how to choose a motor and gear ratio given application requirements.  I will then provide information about choosing a gearbox, followed by an overview of the motors and gearboxes available in FRC.  Finally, I will demonstrate how to use what you learn in this tutorial in an example problem and point out extra tools and resources if you want to learn more.

This tutorial was made through the Autodesk FIRST High School Intern program.

Prerequisites
A basic understanding of physics – e.g. force, torque, power, and gear systems
A willingness to learn
 
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Step 1: Motor Characteristics

Picture of Motor Characteristics
There are several important characteristics of motors that provide information about a motor and its capabilities.  They are the motor’s output torque, its current draw, its output speed, its power, and its efficiency, each of which I will discuss in turn.  These characteristics are interdependent and can all be derived from four values: the motor’s stall torque, stall current, free current, and free speed.
 
Torque
A motor’s output torque is the amount of force with which its output shaft can rotate.  If too much torque is applied to a motor, its output shaft will stall, or stop turning.  Other motor characteristics are commonly written as a function of torque.  It is usually measured in N-m when metric units are required and oz-in when English units are required.
 
Current Draw
The motor’s current draw is the amount of electrical current the motor draws at any given load.  As the load on the motor (the torque) increases, the amount of current that the motor draws increases linearly.  This relationship can be written as
 
(1)   
 
Symbol Name Units Description
I Current Amps (A) The amount of current drawn by the motor
Istall Stall current Amps (A) The amount of current drawn when the motor is stalled
Ifree Free Current Amps (A) The amount of current drawn when the motor has no load placed upon it
τstall Stall Torque Newton Meters (N-m) The amount of torque required to stall the motor
τ Torque Newton Meters (N-m) The amount of torque applied to the motor output shaft
 
Speed
The motor’s output speed is the rotational velocity at which the output shaft spins.  As the load on the motor increases, the output speed decreases linearly.  This relationship can be written as
 
(2)   
 
Symbol Name Units Description
ω Speed Rounds per Minute (rpm) The rotational velocity of the motor’s output shaft
ωfree Free Speed Rounds per Minute (rpm) The speed at which the motor spins when it has no load place upon it
τstall Stall Torque Newton Meters (N-m) The amount of torque required to stall the motor, or prevent its output shaft from rotating
τ Torque Newton Meters (N-m) The amount of torque applied to the motor output shaft

Photo Credit: http://www.engin.umich.edu/group/ctm/examples/motor/motor.html
peterrifken19 days ago

Hello, I'm having trouble viewing the images (formulas) when downloading this as a PDF. Is anyone else having trouble and if so, found a workaround? Thanks!

juliadee2 years ago
This is good. Would love to see a follow-up about actually building geartrains - best practices for making a "breadboard" with parallel plates, sources for gears, axles, bearings, etc.
FIRSTIntern (author)  juliadee2 years ago
I posted an Instructable about how I made a gearbox here - it's kind of the same topic, but doesn't go into quite the detail it sounds like you want.
It's definitely a good idea though - I'll put it on my list of ideas for future tutorials.
Great tutorial! Oh yes, I definitely would like to learn more about how to connect wheels to a motor and bearings as well :-) Good luck with your study!
actimm2 years ago
What is the difference between torque and stall torque when dealing with an electric motor? As I recall, the highest torque rating of an electric motor is it's stall torque. I thought separating them out was more a function of usable power in an IC engine rather than an electric motor. Or is that formula generic, it's been a dozen plus years since I've even had to look at that stuff.

Also, are you going to get into the differences between DC and AC motors? I seem to recall there being a couple of differences when you start talking about what you want the motor to actually do. BTW, not to sound like a jerk, but I do mean differences beyond what source of electricity is handy.
FIRSTIntern (author)  actimm2 years ago
To answer your second question, the reason why I did not discuss AC motors is twofold. First, this tutorial was meant for students who are part of the FIRST Robotics Competition, which only allows brushed DC motors, though the theory is definitely applicable to any project that uses DC motors. Second, I would have no idea what I was talking about if I tried to cover AC motors. I have never used them, so I might be giving unreliable information if I tried to teach about them.

If I understand your first question correctly, a brushed DC motor's output torque is not equal to its stall torque. Instead, it applies as much torque as is necessary to rotate the motor's output shaft. In other words, stall torque is a constant that is a characteristic of the motor, while torque is the amount of torque the motor is outputting at a given speed/current.
belsey2 years ago
I'd been waiting for an instructable like this... For a long time I've wanted to attempt building a solar powered plant stand/turntable which would slowly rotate (about 180° in 24 hours) but I never knew where to start. Though it is still daunting, at least now I know where to begin!
I'm no expert but I think a servo might be better for something like that.
Re-design2 years ago
Most excellent work!
FIRSTIntern (author) 2 years ago
Thanks for the feedback! I'm glad you found the information helpful!
Tomdf2 years ago
This is fantastic, I've wanted to learn this stuff but never knew where to start. Thanks, this will be off great use to me!
randofo2 years ago
Very thorough. Nice job.