How much Torque is needed to do Skid Steering

Lynxmotion Rovers, Sumo, and Tracked
1

Hello, I need help in figuring out how much weight can Lynxmotion A4WD1 (lynxmotion.com/p-657-a4wd1-c … omous.aspx) carry
if it is equipped with four GHM-04 motors (lynxmotion.com/p-96-gear-hea … 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 beam-wiki.org/wiki/Steering_Techniques

The Lynxmotion A4WD1 is equipped with four 4.75" (0.12065 m) RC truck tires (lynxmotion.com/p-108-off-roa … -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 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 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 robotshop.ca/drive-motor-tutorial.html
to solve for acceleration as a function of incline angle (units omitted below):

T = (100/e)(a + gsin@)MR/N
0.0981 = (100/30) * (a + 9.81sin@) * 7 * 0.0603 / 4
0.0981 = (a + 9.81sin@) * 0.35175
0.2788 = a + 9.81sin@
a = 0.2788 - 9.81sin@

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

Torque * RPS >= Mass * Acceleration * Velocity * (100/efficiency%) / (2PI) / #Wheels
Where:
Acceleration = a + 9.81sin@ = 0.2788 - 9.81sin@ + 9.81sin@ = 0.2788
Gives:
Torque * RPS >= Mass * 0.2788 * Velocity * (100/efficiency%) / (2PI) / #Wheels
0.0981 * 2.19 >= 7 * 0.2788 * Velocity * (100/30) / (2PI) / 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:
ikalogic.com/tut_mech_1.php
gizmology.net/tracked.htm
But I am unsure of how to take friction into account, and am sincerely hoping for detailed guidance on this…

2

Wow… :open_mouth:

As you already know it’s the friction that is the center of the problem with skid steer. The friction is going to be different depending on what surface the bot is operated on. Tile floor is the best, and plush pile carpet is the worst. If operating outside, sand and gravel is great, tall grass is the worst.

I have never made a serious attempt to quantify what the maximum weight the bot can carry on specific surfaces. Too many variables, etc. So I opted for the conservative approach, list the payload as 5lbs, which was tested on low pile (office) carpet.

Good luck with the math approach.

3

Thanks Robot Dude for the quick reply :slight_smile:

May I ask if at the time of testing (to arrive at the 5lbs payload),
was it the case that the A4WD1 was equipped with GHM-01 (which has smaller torque than GHM-04)?

And since GHM-01’s rated Torque/Load is (620 gf-cm = 0.0608 Nm)
whereas GHM-04’s rated Torque/Load is ( 1 kgf-cm = 0.0981 Nm), which is 1.613 times more “powerful” than GHM-01,
hence can I expect that the A4WD1 equipped with GHM-04 will be able to carry a payload of (1.613*5lbs = 8.065lbs = 3.658 kg)?

I did a quick calculation using the same rearranged Torque relation in robotshop.ca/drive-motor-tutorial.html
based on some of GHM-01 motor’s specs below (worst-case scenario):
Rated Voltage = 12 V
Rated Torque/Load = 620 gf-cm = 0.0608 Nm
Stall Torque = 4.6 kgf-cm = 0.4511 Nm
Speed at Rated Load = 159.3 RPM = 2.655 RPS
Efficiency at Rated Load = 40% to 45%

Giving the following performance for 7kg A4WD1 equipped with GHM-01:

T = (100/e)(a + gsin@)MR/N
0.0608 = (100/30) * (a + 9.81sin@) * 7 * 0.0603 / 4
0.0608 = (a + 9.81sin@) * 0.35175
0.1728 = a + 9.81sin@
a = 0.1728 - 9.81sin@

Under an incline of (0 degree), A4WD1 can accelerate (0.1728 m/s^2) to a velocity of (1.0062 m/s)
Under an incline of (1 degree), A4WD1 can accelerate (0.0016 m/s^2) to a velocity of (1.0062 m/s)
Under an incline of (1.0096 degrees), A4WD1 can accelerate (0 m/s^2)

Which agrees with the analysis that a 7kg A4WD1 (equipped with GHM-04)'s acceleration (0.2788 m/s^2)
is 1.613 times more “powerful” than a 7kg A4WD1 (equipped with GHM-01)'s acceleration (0.1728 m/s^2)

Similarly, below is the performance for a 2.1kg A4WD1 Combo Kit for Autonomous equipped with GHM-01 (I assume it weighs 2.1kg):

T = (100/e)(a + gsin@)MR/N
0.0608 = (100/30) * (a + 9.81sin@) * 2.1 * 0.0603 / 4
0.0608 = (a + 9.81sin@) * 0.105525
0.5761 = a + 9.81sin@
a = 0.5761 - 9.81sin@

Under an incline of (0 degree ), A4WD1 can accelerate (0.5761 m/s^2) to a velocity of (1.0062 m/s)
Under an incline of (1 degree ), A4WD1 can accelerate (0.4048 m/s^2) to a velocity of (1.0062 m/s)
Under an incline of (2 degrees), A4WD1 can accelerate (0.2337 m/s^2) to a velocity of (1.0062 m/s)
Under an incline of (3 degrees), A4WD1 can accelerate (0.0626 m/s^2) to a velocity of (1.0062 m/s)
Under an incline of (3.3666 degrees), A4WD1 can accelerate (0 m/s^2)

May I ask if this analysis (under 30% efficiency assumption)
reflects your observation of A4WD1’s performance during its “testing to arrive at the 5lbs payload”?
If you can still remember :stuck_out_tongue:

Also, may I ask if the A4WD1 during its “testing to arrive at the 5lbs payload”
was able to “turn smoothly” under both Skid Steering techniques: “Spin (In Place Pivot)” and “Hard Turn (Circular Pivot)” ?
Thanks in advance :slight_smile:

4

Yes, the A4WD1 comes with the GHM-01.

No math was involved in the testing of this robot. :stuck_out_tongue:

Yes it was able to move about freely. It’s been a long time…

5

Thanks Robot Dude :slight_smile:

May I ask from your experience, if it it the case that
since GHM-01’s rated Torque/Load is (620 gf-cm = 0.0608 Nm)
whereas GHM-04’s rated Torque/Load is ( 1 kgf-cm = 0.0981 Nm), which is 1.613 times more “powerful” than GHM-01,
hence can I expect that the A4WD1 equipped with GHM-04 will be able to carry a payload of (1.613*5lbs = 8.065lbs = 3.658 kg)?

Also, is it possible to equip Wheel Encoders onto GHM-13 (lynxmotion.com/p-250-gear-he … shaft.aspx) ?
Such as perhaps purchashing some kind of special wheel encoder that can be equipped at the front of GHM-13 ?
Or some other tricks or fancy accessories?
Or is it possible to get a larger gear reduction for GHM-04?
What about PGHM-03? (lynxmotion.com/p-516-planeta … shaft.aspx)
If it can be easily installed into A4WD1 without drilling any extra holes into the chassis.

Basically…may I ask what is the highest torque motor that I can purchase from Lynxmotion website (or other websites)
to equip the A4WD1, but still be able to install a Wheel Encoder onto it?
(I would like my A4WD1 to carry a Mini-ITX PC + Stereo Camera + Batteries to do SLAM research)

Thanks in advance for any advice that you will give :slight_smile:

6

I will agree that the GHM-04 has more torque than the GHM-01, but it’s due to the gear reduction. The motor in the GHM-04 is not as powerful as the motor in the GHM-01. Short of me actually testing this with a real bot, I’m not making any specific claims.

No.

Not that I am aware of.

I only stock what’s on the website. I’m not able to make special orders.

Yes it can be installed. No it can not accept an encoder.

GHM-04