I want to build a 4W robot platform able to deal with difficult terrains. The first step is to make a list of possible DC motors able to push the robot on sand, mud, over rocks, in a forest, in lawns or anywhere else I would like to drive it.

In this article, my objective is to find the theoretical values of torque and RPM for the DC motors. Also, I did a list of DC motors that I can use for this project. I know that matching a motor for a specific application is not easily accomplished through trials and errors. Moreover, the necessity of purchasing and testing many DC motors are inefficient and brings me additional costs. So, I have to determine the optimal DC motor specifications for the functional requirements.

Let’s move a little bit to the functional requirements of the mobile platform. This robot should be able to climb slopes up to 20 degrees, driven by four DC motors connected through belts or shafts to the wheels, supplied voltage = 24 Volts, the diameter of the wheel = 0.35m, and able to reach a maximum speed of 10km/h (6.2 mph). Broadly speaking, these are the functional requirements of the robot.

The key: 24V.

Why 24V? Because the motors are happy at 24V. I know that a 12V DC motor is cheaper than a 24V DC motor. The second advantage is the weight of these electric motors that are lighter than the 24V DC motors. But it is clear to me. I’ll use 24V DC motors.

It does not seem complicated, but it would be a challenge to choose the right DC motors since I have to take into account the weight of the robot as well the minimum working time that I have in mind. I consider that an average of 1.5 working hours on a charge is more than enough for this all-terrain robot.

The batteries, the chassis, and the motors are the biggest problem for the total weight of the robot.

For example, a 12V 55Ah SLA battery weights 17Kg (37 pounds). This battery has a good price in Romania – Europe. It costs around 76EUR. With 12V and 55Ah per battery, I need two of them to have energy for at least one and a half working hour. So, only the batteries will weigh around 35Kg (75 pounds).

I need a strong chassis to carry all the weight and resist to shocks and other external factors. I can estimate that this would have a weight of 15 Kg (33 pounds) without the wheels.

The wheels will have around 0.35m (13.7 inches) in diameters. I found that such a heavy duty wheel could have a weight of 4Kg (9 pounds). Adding the weight of the wheels, there will be a plus of 16Kg (36 pounds).

Four 24V DC motors can cost me another 8 to 10Kg (13 to 22 pounds).

Considering other components, the DC motors will drive a total weight of about 70Kg (154 pounds).

So, I need four powerful DC motors able to drive a weight of 70Kg (154 pounds). Well, I’m not so glad by these numbers, but I have to take this challenge and find the right electric motors for this robot.

#### First step: I calculate the required wheel torque

What I know is:

- Mass = 70Kg
- Acceleration = 2meter/square second

Force(Newtons) = Mass (Kg) x Acceleration (meter/square second)

F= 70Kg x 2meter/square second=140N

The total force required to meet the functional requirement is 140 Newtons. However, the robot has 4 motors and wheels. Therefore, each motor/wheel combination needs only supply quarter the required force or 35 Newtons.

Torque (Nm)= Force(Newtons) x Distance (meters)

In this case, the distance is the wheel diameter/2 (0.35m/2).

Torque = 35N x 0.175m = 6.12Nm

The required torque at each wheel is 6.12 Newton meters.

#### Second step: calculate the required wheel RPM

What I know is:

- Wheel Diameter = 0.35m
- Wheel Circumference = Pi x Diameter = 1.09 meters
- Required Speed = 2.7 meters/second (10km/h)

Speed (meters/second) = RPS (revolutions per second) x Circumference (meters)

RPS= Speed / Circumference = 2.7 / 1.09 = 2.47

RPM = 2.47 x 60 seconds = 148 revolutions per minute

#### A very long conclusion

The required torque at each wheel is 6.12 Newton meters. The DC motors should have at least 148 revolutions per minute.

Taking into consideration the additional losses mainly due to the friction and inefficiency in the power transmission mechanisms and considering that the robot should be able to climb slopes up to 20 degrees, normally I have to take a large margin for torque. For this robot, a fairly large margin is the Newton meters x 2.

I have to find four DC motors with values closer to:

- RPM: 148
- Torque: 2 X 6.12Nm = 12.24Nm

Here is a list of potential DC motors that I can use for this project:

- MY1016Z 350W 24V|36V 10.7Nm DC-Motor Stirnrad-Getriebe FORANDOR
- MY1016ZL DC-Motor Stirnrad-Getriebe 250W|350W 24V|36V 7.8-10.7Nm FORANDOR
- DG-158A 24VDC 135 RPM Wheel Chair Motor Pair

*Disclaimer: The values are only rough approximations. You bear the risk of anything unexpected and trying it. So, please don’t blame me!*

Resources:

Hello. I very much enjoy your blogs, thank you very much. I have just begun researching motors for a home service robot and also a potential security bot. I found this online tool, which helped me to check the size of motors that I need: http://www.robotshop.com/blog/en/drive-motor-sizing-tool-9698

I am a bit concerned, because this tool gives quite different values to what you have calculated (I input all your variables, 70kg weight, 35cm wheel size, 2.7m/s speed, 20 degree slope). Take a look and see what you think?

Also, I wonder if you have considered encoders for the motors that you are buying. Is that something that you need? I think I will need encoders for the motors of my autonomous robot because otherwise it becomes more tricky to accurately define your direction and also how far you’d like to move. I think they may be useful later when I am using ROS (Robotic Operating System) for SLAM and navigation.

Do you have any ideas about encoders. Are you going to add them later?

Thanks again for a great blog!

Hello Grant,

The calculator is totally wrong. I inserted the values and returns me 50 Nm per motor. Since I have four DC motors, the total torque is 200 Nm. 200Nm is a torque much higher than the torque of my car.

I am very enjoyed for this side. It’s a nice topic. It helps me very much to solve some problems. Its opportunity is so fantastic and working style so speedy. I think it may be help all of you. Thanks.