Alexander Robotics

After sketching my idea for a robot, I was left with several unknowns: what to use for the brains, the muscle, the power, the frame. I opted to approach the “muscle” first.

After reading the exceptional Robot Building for Beginners and several robot building tutorials online, I was still left perplexed when selecting a DC motor. How much torque is needed and what’s an acceptable RPM were my two top questions. A helpful tutorial by Society of Robots, Robot Dynamics, helped me calculate the specifications I would need in a motor.

Motor calculations

Rather than repeat the knowledge expressed in Robot Dynamics, I present to you my actual calculations and decisions that influenced them.

The first specification to calculate was the RPM of the motor.

RPM = velocity / wheel circumference

My target speed for the robot was slightly faster than an adult’s average walking speed (approximately 80 m/min). I added an arbitrary 20 m/min to be “slightly” faster. I also assumed a wheel diameter of 0.076 m, roughly the size of an inline skate wheel.

The resulting RPM calculations were

RPM = (100 m/min) / (3.14 * 0.076 m) = 419 RPM

Next, I needed to calculate the torque requirements.

torque = force * distance

A Newton is a measurement of force, which I tackled first.

force = mass * acceleration

I expected the robot to weigh about 14 kg with payload. For acceleration, I summed two values: the acceleration on a flat surface and the acceleration on an incline. I took the tutorial’s advice for the flat acceleration.

acceleration for flat plane ≈ half velocity ≈ 0.080 m/sec^2

The incline formula calculates the acceleration needed to overcome gravity at an angle so the robot won’t fall backwards.

acceleration for incline = gravity * sin (theta * pi/180)

I assumed an angle of 20°.

9.81 m/sec^2 * sin (20 * pi / 180) = 0.335 m/sec^2

The final calculation was 0.80 m/sec^2 + 3.355 m/sec^2 giving a total acceleration of 4.155 m/sec^2. As can be seen, an incline drastically impacts the force required.

With the mass and acceleration, I calculated the force requirements.

force = 14 kg * 4.155 m/sec^2 = 30.17 newtons

The distance in the torque value derives from the distance between the wheels axis and where the force is applied. In other words, the distance is the wheel’s radius.

distance = wheel's radius = 0.038 m

I estimated the total torque and the torque per motor at

torque = 30.17 N * 0.038 m = 1.146 N m torque per motor = 1.145 N m / 2 = 0.573 N m 

Motor selection

With the required RPM and torque (419 RPM and 0.573 N m, respectively), I had the criteria needed to select a motor.

I started with basic googling for robot motor, robot motor store, and so forth. A few good sites in terms of selection and details were Robot Market Place, Pololu, and Lynxmotion. These pages often use different units for measuring torque, like kg-cm or oz-in. An online torque conversion chart will help.

I ended up selecting the motor from Pololu. Pololu had the same motor with different gear ratios, allowing me to choose more torque or more speed. The closest matching motor was the 29:1 geared DC motor. (Full disclosure: I actually bought two 67:1 geared motors because of an original miscalculation.)

An important motor selection criteria I did not use in my above calculations was voltage. Honestly, I didn’t care at this stage. If a 6 V motor met my requirements, perfect. Ideally, I wanted a motor between 6 and 12 V, but I would be willing to go up to 24 V. My power supply planning would come later.

Please contact me if you notice an inaccuracy in the calculations. I’ll update the post as needed.