How do you Calculate Overall Ratios with Pulleys and Geared Motors?

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Daniel Cartledge
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Posted on Thursday, January 5, 2006 - 11:22 pm:    Edit Post    Move Post (Moderator/Admin Only)

I am wanting to use a large single ratio gearbox on my robot but am unsure of the correct ratio.
I currently have some time pulleys and belts. The one on the motor has 10 teeth and the 2 wheels(2 on each side)have 30 teeth joined by a pulley belt that is of 545mm circumference.The wheels are 110mm. First of all i would like to know what ratio gearbox i should use to make it go around 8-12 mph. As i'm not too sure about this i think it should be either 10:1 at around 800rpm or 50:1 at around 200rpm. Most of my confusion is towards how the two gearing relate to each other such as the 3:1 from the pulleys being*towards the gear ratio or added to it. Sorry for going on a bit but i hope you can answer my question. Thanks.
Admin (Admin)
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Username: Admin

Post Number: 108
Registered: 10-2004
Posted on Friday, January 6, 2006 - 6:57 pm:    Edit Post    Move Post (Moderator/Admin Only)

Daniel,

Firstly you need to find out the overall ratio you need. We know the wheel diameter, we know the desired speed say 10 mph, what you have not advised is the motor speed let's assume 10,000 rpm.

Now, use the new robot speed calculator on the main Technobots site. See http://www.technobots.co.uk/Technical/Calculators/Speed%20calc/Speed%20calc.htm or simply click the 'Calculators' button on the top navigation bar. Enter in the above details (or your actual motor speed) into the table and for 10,000 rpm you get 12.88:1.

Different stages of gearboxes are multiplied together and as you say, your pulley ratio is 3:1 so your gearbox stage needs to be 12.88/3 = 4.3:1.

You can double check the ratio with our Gearbox Calculator which can also be found in the Calculators section. In the 'User Defined' column, enter 10 for the motor drive, 30 for the stage 1 driven, then enter 1 for the stage 2 drive and 4.3 for the stage 2 driven. In this case, actual numbers do not matter, it's the ratio that counts. Then select 2 in the 'Number of Stages' drop down box and you should get an answer of 12.9 which is what we wanted.

Now you need to ensure you use an accurate motor speed to determine the gearbox ratio.
Daniel Cartledge
Unregistered guest
Posted on Friday, January 6, 2006 - 7:29 pm:    Edit Post    Move Post (Moderator/Admin Only)

Thanks for the advice.I am grateful for the info and now think i have the right idea of motor but just incase i would like you to double check. Wanting to go 10mph with wheels of 110mm diameter i have found a motor i feel would work, which has a ratio of 2.5:1 and at 12volts runs at 6300rpm. So just to be clear the 2.5:1 times 3:1 gives 7.5:1 and using you calculator i have found that the perfect gear ratio is 8.12 so i feel this should be just fine but as i say would like clarification. Thanks again.
Admin (Admin)
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Username: Admin

Post Number: 112
Registered: 10-2004
Posted on Friday, January 6, 2006 - 8:16 pm:    Edit Post    Move Post (Moderator/Admin Only)

Daniel,

Happy to help. Entering 6300 rpm, 7.5:1 (2.5 x 3), 110mm into the Robot Speed Calculator gives a speed of 10.8 mph so yes, perfect as long as the motor is of sufficient power.

Just one point, not knowing what geared motor you are looking at, make sure the rpm is the motor speed and not the geared motor output speed. For example, our 919D 2.5:1 motor has an output speed (after the 2.5:1 reduction) of 6300 rpm (sounds like this is the motor!) This speed will only be reduced by a further 3:1 from your pulley system. This means a speed of 27 mph.

When we say motor speed, it is the speed of the motor before any gearbox reduction. I would suggest if looking at the 919D range:

Motor speed 15,800 (see motor data for the 919D)
wheel 110mm, desired robot speed 10mph gives a gear ratio of 20.36:1 which divided by 3 gives 6.78:1. Nearest being 6:1 which fed back in to the calculator as 3 x 6 18:1 gives a speed of 11.3 mph.
Daniel Cartledge
Unregistered guest
Posted on Friday, January 6, 2006 - 8:54 pm:    Edit Post    Move Post (Moderator/Admin Only)

So you are recommending that i should use the 6:1 gearbox motor at 12v and you are saying that the shaft spins at 6,300 not the motor. I did think it was like that. That motor is the one i'll be buying. Yet again i appreciate help. Regards Daniel. Also in your email how have you achieved to get a speed of 27 mph with the same input i used how do you achieve it and also why have you at one point put motor speed 15800 when i think all the motors on that page aren't that fast. Thanks again.
Admin (Admin)
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Username: Admin

Post Number: 113
Registered: 10-2004
Posted on Friday, January 6, 2006 - 9:48 pm:    Edit Post    Move Post (Moderator/Admin Only)

Yes Daniel, use the 6:1 based on the info you have provided. The 919D uses the 540/1 motor (see the table at the top of the 919D page). At 12V you get 15,800 rpm what ever the ratio (in theory). Enter 15800, 7.5:1 (2.5 x 3) and 110mm into the calculator and you get 27.1 mph.
Daniel Cartledge
Unregistered guest
Posted on Friday, January 6, 2006 - 10:07 pm:    Edit Post    Move Post (Moderator/Admin Only)

Using the 6:1 motor at 12v will give a speed of 6300rpm i think so now wouldn't i use 6:1(the motor reduction) times 3:1(the pulley reduction) making 18:1? Meaning to get the wanted 10 mph the motor shaft would have to be spinning at 13971rpm which isn't possible unless the motor is ran at 24v. Am i correct or not?
Admin (Admin)
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Username: Admin

Post Number: 114
Registered: 10-2004
Posted on Saturday, January 7, 2006 - 9:48 am:    Edit Post    Move Post (Moderator/Admin Only)

Daniel, if you refer to the Technobots page on the 919D at http://www.technobots.co.uk/contents/en-uk/d424.html part number 1450-051 you will note that the output speed of the 6:1 motor @ 12V is 2633 rpm (15,800 / 6). If you prefer, feed this into the calculator with a 3:1 final drive ratio and your wheel diameter of 110mm and you get the same robot speed of 11.3 mph. Or enter 15,800 with a 18:1, wheel diameter of 110mm and you get 11.3 mph. I am afraid there is little else I can add to this. Can I suggest that you work your way through the sums, I'm sure you will find them to be correct.