Gearing sums need someone to check over please

[TheBadger]

Hi

So I am not very skilled at all at mechanics, but using the tutorials on this site I have just gone through my gearing sums for my robot, I have to make the gear box myself (or get it made) so I really don't want to have it made to realise my maths was crap in the first place.

I know its a bit of an ask but hopefully someone would be able to have a glance over them and see if it all makes sense.

Thanks anyway.

Right so, My robot is approx 1kg, It will be a white line follower so speed isnt exactly paramount, but it will be in a race so I can't have it going deadly slow, the motors and wheels are given to us and cannot be changed.

So,

Motors: 2 of, data sheet says 7800rpm at maximum efficiency with 20g/cm torque and 130g/cm stall torque.
Wheel diameter = 75mm
The track is about 2m of flat and then 2m of 20degree incline.

So these are my sums for the gearing.

First off, Acceleration required for the incline, 9.81*sin(20*pi/180) = 3.35m/s^2
So with the relationship given on the site, (acceleration to velocity should be 1:2), I picked a Velocity of 6m/s (little lower than 2 but I thought it would be okay)

Velocity of robot is 7800rpm x 0.075m = 1837m/minute = 30m/s

Force needed for the incline = mass (1kg) x 3.35 = 3.35N

Force capable of motor = Torque/Wheel radius = 20/3.75 = 5.3N

So the gearing.

Torque old (20g/cm) x Velocity old (30) / Velocity new(6) = Torque new  = 120g/cm

Is this right? so I need a 1:5 gear ratio (30/6 = 5)

Or is there something in there which is just stupid, like should I be using stall torque and also will 120g/cm even shift a 1kg robot up a 20degree incline.


I am really trying to get this robot off the ground but I have no experience of mechanics.

Thanks for any help at all!!!

[Soeren]

Hi,

[...] data sheet says [...

Could you post the data sheet or a link to it?

How many turns and at what angle/diameter are on the track?
What's your wheel base (forward-back and left-right)?
How fast reacting is your line sensor?

It's the turns, how (well) you read them and how you accelerate out of them that matters most in a line follower.

Just read your post very briefly (since I didn't had a data sheet ), but do you really want to accelerate up-hill on the incline(s)?

And...
"mass (1kg) x 3.35 = 3.35N"
I get it to 32.85N

(1N = 101.972g)

[TheBadger]

Hi,

[...] data sheet says [...

Could you post the data sheet or a link to it?

How many turns and at what angle/diameter are on the track?
What's your wheel base (forward-back and left-right)?
How fast reacting is your line sensor?

It's the turns, how (well) you read them and how you accelerate out of them that matters most in a line follower.

Just read your post very briefly (since I didn't had a data sheet ), but do you really want to accelerate up-hill on the incline(s)?

And...
"mass (1kg) x 3.35 = 3.35N"
I get it to 32.85N

(1N = 101.972g)

Thanks for the reply, Okay onto some answers.

There is 1 turn on the track, it comes about a 1m from the top of the incline, I haven't got the angle on me but it is not very sharp at all, the turn is about 30-40cm long, It isn't meant to be too challenging.

The wheel base is left- right 200mm
and then there is a castor which is 300mm away from those.

The line sensor is 5 of these http://www.vishay.com/docs/83760/tcrt5000.pdf fed into a darlington and then into a schmitt trigger, it is pretty quick to respond.

And the motor is this

http://docs-europe.electrocomponents.com/webdocs/0032/0900766b8003209c.pdf  (It will be running at 5V, this has been done before with no problems in past with others using same motors, So I just took my data off the 3V 7800rpm etc)

Regarding the acceleration up hill, I just took that off the tutorial on the main site, I thought I would need that to counteract gravity. I took everything off the tutorials really.

Thanks again.

[Conscripted]

And the motor is this

http://docs-europe.electrocomponents.com/webdocs/0032/0900766b8003209c.pdf  (It will be running at 5V, this has been done before with no problems in past with others using same motors, So I just took my data off the 3V 7800rpm etc)

What are you using as a power source for the motors? It may not be a good idea to run them off the same source as your logic. What are you using for a battery?

If you run the motors at a higher voltage then the data on the data sheet you are going to get different numbers. When you apply a higher voltage the motor will spin faster. Because you appied more power the current (and torque) will go up as well. Just be careful not to over do it.

Good luck with your project.

Conscripted.

[TheBadger]

And the motor is this

http://docs-europe.electrocomponents.com/webdocs/0032/0900766b8003209c.pdf  (It will be running at 5V, this has been done before with no problems in past with others using same motors, So I just took my data off the 3V 7800rpm etc)

What are you using as a power source for the motors? It may not be a good idea to run them off the same source as your logic. What are you using for a battery?

If you run the motors at a higher voltage then the data on the data sheet you are going to get different numbers. When you apply a higher voltage the motor will spin faster. Because you appied more power the current (and torque) will go up as well. Just be careful not to over do it.

Good luck with your project.

Conscripted.

Hi

Thanks for the input but this is all not a problem, the motor will be driven off a H bridge which is optically isolated from the logic circuit.
The whole circuitry has been used before 100's of times, the only problem I am having is with these gear calculations.

[hopslink]

You are on the right track, but you have made a couple of errors. One is a units mix-up and the other is changing from a force based to speed based calculation without working completely through the problem. Unfortunately you don't get to choose top speed and acceleration with a fixed motor, you trade one against the other.

6m/s is crazy fast for a line follower and you will find you will never see that with the constraints you have. You need to calculate from the constraints, which are your 'bots mass, the motor you have, and the incline on the course.

3.42 m/s² is the decceleration due to gravity your bot must overcome to move up a 20 degree slope, so to give it a little leeway (but mostly to make the maths easier ) call your minimum acceleration requirement 4m/s². Since you have 2 motors you want each to deliver enough force for a 2m/s² acceleration.

Now convert required acceleration to force:
F=MA = 1kg x 2m/s² = 2N

And compare to the force your motors provide (running, not stalled):
Torque=20g.cm at motor = 20/3.75 = 5.33g(F) (thats grams force, not Newtons  ) at the wheel.

so convert g(F) to Newtons:
1N ~100g(F) so 5.33g(F) = 0.0533N

Desired gear ratio will be the ratio of force provided:required -
= 0.0533:2 = 1:37.5

Now you can take the gear ratio and calculate your speed:
Speed = ((motor_rpm/60) x pi x wheel_diameter) / gear_ratio = ((7800/60) x 3.14 x 0.075)/37.5 = 0.82m/s

Speed may seem low but this is not too bad for a line follower, and if you try to go much faster you run the risk of your 'bot not being able to drive up the incline, or track the line properly. You should get more points for a slow finish than a quick failure. If you want more performance try to remove some mass from your 'bot, halve your mass and you double your acceleration for a given motor.

N.B. Approximations used throughout and no allowance made for system inefficiency.