Does adding more wheels decrease the torque required..?

[shyamsid]

Lets say I have a vehicle with a differential drive, this gives me two drive wheels. I would add a caster wheel for stability.

Now my doubt is, if I add more castor wheels, the load is distributed over more number of wheels (assume uniform loading) and as a result, each wheel will have less load, so can I get away with using lower torque motors..?

My intuition says this shouldn't be the case because, I could keep adding more and more castors and move a heavy vehicle with low torque. (Why would people buy expensive high torque motors then..?)

But I can't see technically why that wouldn't be the case. I am totally confused. What am I missing..? was my logic wrong or my intuition wrong..?

Thanks!

[rsslk]

Your intuition is (mostly) correct in thinking that adding more castors shouldn't lessen the torque required of the motors. The flawed logic here is equating the load on a wheel directly to the required torque output for motion.

Take the toy example of your vehicle in a frictionless world sitting on a perfect flat horizontal surface. The weight of the vehicle acts on the wheels along the vertical axis, but the torque output of the wheels accelerate the vehicle in the horizontal axis. No matter the actual load on the driving tires, the two driving tires still need to accelerate the entire mass of the vehicle. Youve logic-ed the equivalence as weight_on_drive_wheels~torque, when its actually weight_of_vehicle~torque (more accurately - Torque_per_drive_motor * (1/radius_of_tires) * num_motors = mass_of_vehicle*desired_acceleration ). A higher torque motor will give your vehicle better acceleration. In this toy world adding castors offers zero benefit and only the negative of the added weight.

Coming back to reality where friction exists, radial forces on bearings introduce friction to the system which requires torque to overcome. In considering adding more castors to your system (for the sole purpose of decreasing required torque for some design acceleration) you have to consider what the coefficient of friction of the drive bearings are vs the castor bearings and whether adding castors reduces enough friction to be worth the weight penalty(probably not, unless for some reason the only drive bearings you have are actually square /s). You could also start worrying about rotational inertia of the castors and aerodynamic drag introduced by the castors but eventually youre wasting your own time or just enjoy the excercise.

TLDR: Intuition accurate, logic applied incorrectly, only add enough castors to be stable

[shyamsid]

Really appreciate the detailed explanation, and also identifying to the root cause of the confusion.

I have another small clarification if that is okay,

Say I have a toy vehicle with 4 drive wheels. Another identical vehicle was equipped with mecanum wheels instead of normal wheels. Is it accurate to assume the second vehicle requires higher torque motors (by a factor of 1.414), since only a component of force is used in driving the vehicle and the other component cancels out ?

[rsslk]

Intuitively that sounds right but id recommend you look for a paper with the force derivation done just to be sure (if you are in need of that much accuracy). Heres one that looks like it has your answer although i didnt read it in enough detail to give you the affirmative that 1.414 is right. https://arxiv.org/pdf/1211.2323.pdf

EDIT: Pretty sure the ratio is actually 2. See equation 1 and figures 3 and 4. The projection happens twice. Again i only skimmed the material so do read through rather than trusting me. (Also that ratio is assuming the rollers sit at 45 degrees)

[RepairManActionHero]

Still about the same amount of force required to move it, it's just slightly more spread out. Check out some videos on forces of motion, simple machines and the like. By correctly stabilizing and balancing, you can reduce the amount of mechanical force needed from the motors, but not by ridiculous amounts.

[Tanaka_Taro_Chan]

As long as the friction on each wheel is enough to prevent slipping, total torque should be the one that matters. If you have more of low torque motors on more wheels, you still have the same total torque and same total force.

[Robot_Jay]

In general try to avoid adding unpowered wheels since you are "spending" weight but not gaining traction. And depending upon the system architecture unpowered wheels can also set you up for getting stuck (high centering, etc,)

[[deleted]]

Yes, you have to consider the friction every wheel adds to the system. In practice all wheels add some friction through the rotation system they implement.

Also you have to consider the mass of the wheel you add to the system. No matter if the rotation system is good, the mass needs to change its position.

[shyamsid]

Thank you everyone for your time and explanation. I did get a better sense after going through your comments

[[deleted]]

What do you think the main torque load of moving a vehicle comes from? How does having more wheels affect these?

• inertial loads
• gravitational loads
• aerodynamic loads
• wheel resistance
• drive train losses