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View Full Version : [Question(s)] How much Torque is needed to do Skid Steering



vsming
09-29-2010, 04:04 PM
Hello, I need help in figuring out how much weight can Lynxmotion A4WD1 (http://www.lynxmotion.com/p-657-a4wd1-combo-kit-for-autonomous.aspx) carry
if it is equipped with four GHM-04 motors (http://www.lynxmotion.com/p-96-gear-head-motor-72vdc-501-175rpm-6mm-shaft.aspx)
but still be able to "smoothly" perform Skid Steering (a.k.a. Tank Steering)
such as Spin (In Place Pivot) and Hard Turn (Circular Pivot) according to http://www.beam-wiki.org/wiki/Steering_Techniques

The Lynxmotion A4WD1 is equipped with four 4.75" (0.12065 m) RC truck tires (http://www.lynxmotion.com/p-108-off-road-robot-tire-475d-x-2375w-pair.aspx)
and its total mass is around 2.1kg (wheels + chassis + electronics).

Below are some of GHM-04 motor's specs (worst-case scenario):
Rated Voltage = 7.2 V
Rated Torque/Load = 1.0000 kgf-cm = 0.0981 Nm
Stall Torque = 7.1000 kgf-cm = 0.6963 Nm
Speed at Rated Load = 131.4 RPM = 2.19 RPS
Efficiency at Rated Load = 40% to 45%

I would like the A4WD1 to carry a payload of at least 4.9kg (giving a total mass of 7kg),
and I estimate its expected efficiency to be 30%,
because GHM-04's efficiency is already around 40%, so (40% * 75% = 30%)

Using RobotShop's calculator in http://www.robotshop.ca/dc-motor-selection.html
with the given input (7kg, four 0.0603m radius tire, 30% efficiency)
to produce the desired torque of 0.0981 Nm (GHM-04's rated torque),
and using the RMF equation in http://www.societyofrobots.com/mechanics_dynamics.shtml
I obtain the following performance:

Under an incline of (0 degree ), A4WD1 can accelerate (0.2788 m/s^2) to a velocity of (0.8299 m/s)
Under an incline of (1 degree ), A4WD1 can accelerate (0.1075 m/s^2) to a velocity of (0.8299 m/s)
Under an incline of (1.628 degrees), A4WD1 can accelerate (0 m/s^2)

Which are obtained by rearranging the Torque relation in http://www.robotshop.ca/drive-motor-tutorial.html
to solve for acceleration as a function of incline angle (units omitted below):

T = (100/e)*(a + g*[email protected])*M*R/N
0.0981 = (100/30) * (a + 9.81*[email protected]) * 7 * 0.0603 / 4
0.0981 = (a + 9.81*[email protected]) * 0.35175
0.2788 = a + 9.81*[email protected]
a = 0.2788 - 9.81*[email protected]

And using this acceleration into the RMF equation in http://www.societyofrobots.com/mechanics_dynamics.shtml
to solve for velocity (units omitted below):

Torque * RPS >= Mass * Acceleration * Velocity * (100/efficiency%) / (2*PI) / #Wheels
Where:
Acceleration = a + 9.81*[email protected] = 0.2788 - 9.81*[email protected] + 9.81*[email protected] = 0.2788
Gives:
Torque * RPS >= Mass * 0.2788 * Velocity * (100/efficiency%) / (2*PI) / #Wheels
0.0981 * 2.19 >= 7 * 0.2788 * Velocity * (100/30) / (2*PI) / 4
0.2148 >= Velocity * 0.2588
0.8299 >= Velocity

This seems to suggest that A4WD1 is able to carry a total mass of 7kg,
and still achieve an acceleration of 0.2788 m/s^2 (at best)
without overheating the four GHM-04 motors under its 0.0981 Nm rated torque/load.

However, I believe this calculation is only valid when A4WD1 is "travelling in straight lines"
and I am unsure of how to calculate for the case when A4WD1 needs to perform Skid Steering
such as Spin (In Place Pivot) and Hard Turn (Circular Pivot).

I am sincerely hoping for some advice on how to calculate the amount of Torque needed to do Skid Steering...
because based on my experience, 4 Wheeled Robots are unable to "turn smoothly"
where the main cause seems to be due to friction, according to both websites below:
http://www.ikalogic.com/tut_mech_1.php
http://www.gizmology.net/tracked.htm
But I am unsure of how to take friction into account, and am sincerely hoping for detailed guidance on this...

cire
09-30-2010, 04:18 PM
You won't be able to calculate anything unless you know the coefficient of friction between your wheel the the surface you are driving on. The less friction, the easier it will be to rotate.

a quick simple calculation you could do is calculate if your motors are strong enough to spin the wheels if the body of the robot cannot move forward, if you can do this then you can definitely skid turn. Unfortunately this won't get you exact numbers required to turn since there's some more math you can do based on your wheel layout I believe...

Anyways, to calculate it take your coefficient of static friction and multiply that by your weight, and that will give you the force required to break away from the static friction.

Ustatic * mass * gravity = breakaway force (cannot be greater then your torque * radius of wheel)

Another thing you can do is buy a set of omni wheels instead for the front of back of the bot, then your wheels wont have to skid.

Anyways, I hope that helps

~Cire

robodork
11-27-2010, 06:00 PM
I may be able to help out once I get back home on Monday. You will want to look for something called the "tankers' equation" or something similar sounding. However, you will want all of the power you can contain. You will have extremely varied results based on the surface. Our robot in college (about 8 kg) needed to drive on astroturf, but we had only tested it on carpet and vinyl. Needless to say, the coefficient of friction varies for the wheels (depends on the surface, or how tightly the surface is affixed to its substrate). We ended up just wrapping the RC truck tires with duct tape to make them slick enough to perform. If it helps, we learned that rotary encoders are essentially useless on a wheeled skid-steer vehicle. That was my experience. Again, I'll check my old stuff to see what we did for sure.

darkback2
11-27-2010, 06:35 PM
I found this, but there was a calculator thingy that I found before, but can't find now.

http://www.scribd.com/doc/38698/Sizing-Electric-Motors-for-Mobile-Robotics

DB