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Drive Motor Sizing Tutorial

RobotShop, June 2008

This tutorial is intended to complement RobotShop's Drive Motor Sizing Toolby providingyou with a step by step explanation as to the calculations behind the dynamic tool. In the

image below hal! a mobile robt is shown. "lthough in this scenario only two out o! the

!our wheels are driven the e#uations below can be used !or any number o! passive anddriven wheels as well as !or tan$ trac$s. The e#uations are presented without units %units

are presented with the drive motor selection tool&.

To calculate the re#uired tor#ue power current and battery pac$ re#uired by a wheeled

mobile robot there are several principles that must be understood concept o! vectors( )D*orce balance( +ower( ,urrent and -oltage. I! you do not understand these concepts you

are encouraged to research them prior to reading this tutorial.

In order to roll on a horizontal sur!ace a wheeled robots motors must produce enough

tor#ue to overcome any imper!ections in the sur!ace or wheels as well as !riction in themotor itsel!. There!ore theoretically a robot %small or large& does not re#uire much tor#ue

to move purely horizontally. /bviously there will be more !riction and resistance in a largerobot than in a small robot though it is still exponentially less than when a robot encounters

an incline.

In order !or a robot to roll up an incline at a constant velocity %no acceleration or

deceleration& it must produce enough tor#ue to 0counteract1 the e!!ect o! gravity whichwould otherwise cause it to roll down the incline. /n an inclined sur!ace %at an angle theta&

however only one component o! its weight %mgxparallel to the sur!ace& causes the robot to

move downwards. The other component mgyis balanced by the normal !orce the sur!ace

exerts on the wheels.
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In order !or the robot not to slide down the incline there must be !riction between the wheeland the sur!ace. The motor in a heavy truc$ may be able to produce )23 horsepower and

signi!icant tor#ue but we have all seen %in person or in video& large truc$s simply spinningtheir wheels as they !all bac$wards on an icy street. It is !riction %f& that 0produces1 the

tor#ue.

The tor#ue %T& re#uired is

To select the proper motor we must consider the 0worst case scenario1 where the robot isnot only on an incline but accelerating up it.


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4ote now that all !orces %F& are along the x and y axes. 5e balance the !orces in the x6direction

Inserting the e#uation !or tor#ue above and the e#uation !or mgx we obtain

Rearrange the e#uation to isolate T

This tor#ue value represents the total tor#ue re#uired to accelerate the robot up an incline.

7owever this value must be divided by the total number %N& o! drive wheels to obtain thetor#ue needed !or each drive motor. 4ote that we do not consider the total number o!

passive wheels as they have no e!!ect on the tor#ue re#uired to move the ob8ect aside !rom

adding weight.

The !inal point to consider is the e!!iciency %e& in the motor gearing and wheel %slip&.

This increases the tor#ue re#uired and compensates !or ine!!iciencies.

Total power %P& per motor can be calculated using the !ollowing relation


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T is $nown !rom above and the angular velocity %w& is speci!ied by the builder. It is best to

select the maximum angular velocity to be able to !ind the corresponding maximum power.9nowing the maximum power and the supply voltage %V& which the builder chooses we

can !ind an idea o! the maximum current %I& re#uirements

The two e#uations above are used to produce the !ollowing relation

*inally the capacity %c& o! battery pac$ re#uired can be estimated using the e#uation

:ou may wonder why such a large value is needed. This is because when choosing abattery pac$ the rated amp hours are not an accurate indicate o! the maximum current the

pac$ can produce !or extended periods o! time. "lso the total charge is rarely retained over

time. This way you will ensure the battery pac$ you select will be capable o! producing thecurrent your motors re#uire !or the time you re#uire and with the ine!!iciencies inherent in

recharging battery pac$s.

4ote This is the battery re#uired +;R M/T/R. To obtain a total battery pac$ re#uired !orthe robot multiply this value by the number o! drive motors.

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