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_TechniquesThe 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.htmlwith 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.shtmlI 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.htmlto solve for acceleration as a function of incline angle (units omitted below):
T = (100/e)*(a + g*sin@)*M*R/N
0.0981 = (100/30) * (a + 9.81*sin@) * 7 * 0.0603 / 4
0.0981 = (a + 9.81*sin@) * 0.35175
0.2788 = a + 9.81*sin@
a = 0.2788 - 9.81*sin@And using this acceleration into the RMF equation in
http://www.societyofrobots.com/mechanics_dynamics.shtmlto solve for velocity (units omitted below):
Torque * RPS >= Mass * Acceleration * Velocity * (100/efficiency%) / (2*PI) / #Wheels
Where:
Acceleration = a + 9.81*sin@ = 0.2788 - 9.81*sin@ + 9.81*sin@ = 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 >= VelocityThis 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.phphttp://www.gizmology.net/tracked.htmBut I am unsure of how to take friction into account, and am sincerely hoping for detailed guidance on this...