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I'm engineering a small (~2 kg and less than 0.125 square meters) vehicle that can traverse sand. I've calculated that my four-wheel vehicle will need two drive motors with at least 30 N-cm (= 43.133 oz-in) of output torque and 20 rpm output speed in order for my vehicle to travel at 10 cm/s which is the average speed I want it to travel at.

I'm having a really difficult time finding suitable brushed, DC motors for my needs, and I want to avoid implementing a gear transmission system if at all possible.

I may end up buying a motor from VEX Robotics that has 167 N-cm of stall torque and 100 rpm no-load speed. Is this an OK thing to do? Can I run these motors at the operating point I need them at or should I just keep looking for a better motor?

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Basically, you are designing your motor to overcome static friction from a standstill. Sand might provide a challenge since you need to worry about angled slopes etc.

I'm going to approach this by providing an example. This should tell you how pick you motor correctly. However, you will have to adapt to your situation. For example, you said you wanted your robot to drive on sand? That will change the friction co-efficient.

enter image description here enter image description here

If the robot is to move and over come static friction from a halt, the weight of the robot must be such that the maximum torque or stall torque is bigger than the force of friction. Below friction is proportional to the weight of the robot:

enter image description here

For this particular application Tstall = 85oz-in = 5.3125lb-in and the rwheel = 45mm = 1.77in. Therefore, Fstall = 3 lb. If the co-efficient of friction is <= 1, then the robot has to be < 3lbs in weight. A more liberal answer is obtained by multiplying by 2 since the robot has two motors => 6lbs.

The motors specs are from this motor:

https://www.pololu.com/product/2286

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For a DC motor 'no load speed' is roughly proportional to voltage, and 'stall torque' is roughly proportional to current, so yes you can use an oversized motor if you reduce maximum voltage and current from the rated specs.

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