### Author Topic: Calculating Stability  (Read 10086 times)

0 Members and 1 Guest are viewing this topic.

#### airman00

• Contest Winner
• Supreme Robot
• Posts: 3,653
• narobo.com
##### Calculating Stability
« on: July 26, 2007, 04:32:52 PM »
How can I calculate how much weight I need to put on a motorized base in order for the robot to be stable? I intend to put  30 pounds on the robot but I need those parts to be at least 4 feet above the base.
What is the calculation for  finding out how much weight I need on the bottom so that the weight on top doesn't cause the robot to tip over?
My base is 18" by 18" with 12.5" wheels. The base can move a maximum of 250 lbs.

Check out the Roboduino, Arduino-compatible board!

www.Narobo.com

#### Robotboy86

• Robot Overlord
• Posts: 139
##### Re: Calculating Stability
« Reply #1 on: July 26, 2007, 05:10:58 PM »
Torque my friend

If you have 30 lbs on top of the robot, 4 feet above the base.. they can exert 4ft*30lbs of torque onto the base.. of 120ft/lbs of torque.  Is 120ft/lbs enough to move your base of 250lbs?

#### airman00

• Contest Winner
• Supreme Robot
• Posts: 3,653
• narobo.com
##### Re: Calculating Stability
« Reply #2 on: July 26, 2007, 06:11:45 PM »
But did you take into account the fact that the base is on wheels?

Does that equation add up with more than one object? If i have object that is 20lbs at 2 ft and object that is 30 lbs at 4 ft, do i do 40 + 120 and then figure it out?
Check out the Roboduino, Arduino-compatible board!

www.Narobo.com

#### Robotboy86

• Robot Overlord
• Posts: 139
##### Re: Calculating Stability
« Reply #3 on: July 26, 2007, 06:30:15 PM »

BEFORE YOU READ THIS!  Remeber, its been 3 years since i've taken physics lol.

The fact that is on wheels DOES factor in, but in your favor.

As far as the weight distrubition it does change several factors..

If you have 20lbs at 2 feet, thats 40ft/lbs of torque, along with 120ft/lbs, which is 160ft/lbs.  Now as far as your wheel base,  if you could provide that, along with its weight(and height) we could determine its ability to resist tipping.

Another key factor though is the size of the base.  If the base itself is 4 feet wide, and 250lbs.. then you could literally take the 30lbs and 20lbs load and lean them off the base, and it would not tip over.  The fact that it is on wheels is in your favor, because it would resist tipping, and would move forward.  Infact, this is how modern SUV's avoid roll overs. If it detects that is leaning past X point it will apply brakes to turn the vehicle INTO the fall, and transfer the motion from side to side, to forward motion(where the suv is far less likely to tip).

#### airman00

• Contest Winner
• Supreme Robot
• Posts: 3,653
• narobo.com
##### Re: Calculating Stability
« Reply #4 on: July 26, 2007, 06:34:00 PM »
Thanks,
can you please give me the equation and tell me what to fill in. Like say V=IR, tell me that V= volts I= current and R= resistance
If you remember the equations
Check out the Roboduino, Arduino-compatible board!

www.Narobo.com

#### Robotboy86

• Robot Overlord
• Posts: 139
##### Re: Calculating Stability
« Reply #5 on: July 26, 2007, 07:46:26 PM »
To be honest the math is kinda ridicilious and I don't remeber it..  your BEST bet though is to make the base dynamic.   Using momentum monitoring(check robotshop.ca for acceloeramators) to determine if it is tilting.. and if it is, then move in the same direction as the tilt.

Otherwise, your base would have to HUGE as hell and heavy to be super stable.

#### hazzer123

• Supreme Robot
• Posts: 460
##### Re: Calculating Stability
« Reply #6 on: July 27, 2007, 01:52:08 AM »
To do this i would -

Calculate how far up the centre of mass from the floor:

Σmx/Σm = [30 * (6.25 + 48) + M * 6.25] / [30 + M]    M = mass at the base
= [1627.5 + 6.25M] / [30 + M]

Calculate how far I would have to tip this to get the centre of mass so that it isnt over the base (tipping point) i have assumed that all the mass is spread evenly.

tan(θ) = opp/adj = 9 / [Σmx/Σm]
= [270 + 9M] / [1627.5 + 6.25M]

θ = tan-1([270 + 9M] / [1627.5 + 6.25M])

Substitute different base mass values into M to get the angle in which your robot could be tipped before toppling over.

eg - no base mass - angle = 9.41 degrees
10lb base mass - angle = 12.03 degrees

I dont have much time to explain it sorry!
Imperial College Robotics Society
www.icrobotics.co.uk

• Supreme Robot
• Posts: 11,680
##### Re: Calculating Stability
« Reply #7 on: August 04, 2007, 09:39:29 AM »
Actually its more complicated than this.

The above stuff handles what is called static stability. That means if your robot isnt moving, will it tip over? Its like standing on one leg and balancing. Or a car just sitting there not moving (or without flipping over with the engine off).

However what you really want is called dynamic stability. This is like running and not falling over. This is also like a car making a sharp turn on a bend in the road without tipping over.

Its a bit hard to calculate and Im too lazy to derive the equations right now, but it involves momentum about the center of mass as well as robot acceleration rates.

Intuitively you want to do this:
• Wide base
• center of mass as close to the ground as possible
• low acceleration rates

One reason it may be hard to calculate is that you may have trouble finding the center of mass of your robot, or you may have some crazy shapped robot. To compensate, after building your robot, just run tests varying acceleration to tweak it until it doesnt flip over.

This is also why I always tell people to keep the batteries at the very bottom of their robots - for dynamic stability.

(hope that helps)