OCCRA
Go to Post One wondered why they couldn't practice in the gym that day - because the robotics team had it reserved was the answer. "Oh, we have a robotics team?" Sigh. This is a team with a low number. They've been around for at least a dozen years. There's still a lot more culture-changing to do. - GaryVoshol [more]
Home
Go Back   Chief Delphi > Technical > Technical Discussion
CD-Events   CD-Media   CD-Spy   FRC-Spy  
portal register members calendar search Today's Posts Mark Forums Read FAQ rules

 
Closed Thread
Thread Tools Rate Thread Display Modes
  #1   Spotlight this post!  
Unread 01-11-2012, 07:28 PM
lemiant's Avatar
lemiant lemiant is offline
the Dreamer
AKA: Alex
FRC #4334 (Alberta Tech Alliance)
Team Role: Leadership
 
Join Date: Feb 2009
Rookie Year: 2008
Location: Calgary, AB, Canada
Posts: 553
lemiant has a reputation beyond reputelemiant has a reputation beyond reputelemiant has a reputation beyond reputelemiant has a reputation beyond reputelemiant has a reputation beyond reputelemiant has a reputation beyond reputelemiant has a reputation beyond reputelemiant has a reputation beyond reputelemiant has a reputation beyond reputelemiant has a reputation beyond reputelemiant has a reputation beyond repute
The physics of flipping

Today I was thinking about how acceleration/deceleration can tip a robot. I know that somehow acceleration acts on the center of mass to flip the robot and this is my theory as to how it works:

The effects of inertia act at your center of mass. They are equal in magnitude, but opposite to the direction of the acceleration of your robot (when you accelerate forwards you will flip backwards).
Mathematically if you add the inertial vector (equal an opposite to acceleration), to the gravity vector, you will get the net vector of your robot. When you project this vector from your center of mass you can determine if a robot will flip. If the projection lands inside the wheelbase you will stay on the ground, but if it lands outside of your wheelbase... prepare to flip. (I have attached some diagrams illustrating this).

Could one of the physics people on these forums, confirm or deny that method (in a strange twist I cannot find the right search term to take me to lessons about this). Also I'm wondering what is a ballpark value for the maximum acceleration a FRC robot sees during a match. And if someone wants to rephrase the above paragraph to use the actual terminology I would be immensely greatful.

Thanks,

- Alex
Attached Thumbnails
Click image for larger version

Name:	3.jpg
Views:	93
Size:	12.5 KB
ID:	11329  Click image for larger version

Name:	2.jpg
Views:	153
Size:	21.9 KB
ID:	11330  Click image for larger version

Name:	1.jpg
Views:	188
Size:	23.3 KB
ID:	11331  
  #2   Spotlight this post!  
Unread 01-11-2012, 08:12 PM
Ether's Avatar
Ether Ether is offline
systems engineer (retired)
no team
 
Join Date: Nov 2009
Rookie Year: 1969
Location: US
Posts: 6,107
Ether has a reputation beyond reputeEther has a reputation beyond reputeEther has a reputation beyond reputeEther has a reputation beyond reputeEther has a reputation beyond reputeEther has a reputation beyond reputeEther has a reputation beyond reputeEther has a reputation beyond reputeEther has a reputation beyond reputeEther has a reputation beyond reputeEther has a reputation beyond repute
Re: The physics of flipping

See Figure1 attached. In this Figure, the vehicle is accelerating just fast enough that the front wheels are about to lift off the floor. In other words, there is no normal force on the front wheels.

The force causing the acceleration of the vehicle is the (horizontal) friction reaction force Ma of the floor on the bottom of the rear wheels.

The weight Mg of the vehicle acts at the Center of Mass (CoM in the figure). The normal force on the rear wheels is Mg.

The torque around the CoM is zero, so Mah = Mgb => a/g = b/h.

If the acceleration is slightly increased, then a/g > b/h and the vehicle will rotate counter-clockwise and tip over backwards.

Last edited by Ether : 01-14-2012 at 03:23 PM.
  #3   Spotlight this post!  
Unread 01-11-2012, 08:17 PM
lemiant's Avatar
lemiant lemiant is offline
the Dreamer
AKA: Alex
FRC #4334 (Alberta Tech Alliance)
Team Role: Leadership
 
Join Date: Feb 2009
Rookie Year: 2008
Location: Calgary, AB, Canada
Posts: 553
lemiant has a reputation beyond reputelemiant has a reputation beyond reputelemiant has a reputation beyond reputelemiant has a reputation beyond reputelemiant has a reputation beyond reputelemiant has a reputation beyond reputelemiant has a reputation beyond reputelemiant has a reputation beyond reputelemiant has a reputation beyond reputelemiant has a reputation beyond reputelemiant has a reputation beyond repute
Re: The physics of flipping

Quote:
Originally Posted by Ether View Post
See Figure1 attached. In this Figure, the vehicle is accelerating just fast enough that the front wheels are about to lift off the floor. In other words, there is no normal force on the front wheels.

The force causing the acceleration of the vehicle is the (horizontal) friction reaction force Ma of the floor on the bottom of the rear wheels.

The weight Mg of the vehicle acts at the Center of Mass (CoM in the figure). The normal force on the rear wheels is Mg.

The torque around the CoM is zero, so Mah = Mgb => a/g = b/h.

If the acceleration is slightly increased, then a/g > b/h and the vehicle will rotate counter-clockwise and tip over backwards.
Do you know what would be a reasonable estimate for the max acceleration of an average robot (12fps top speed, 6wd traction wheels, CIMple gearboxes, 4 CIMs)?

PS What do you use to make those pretty diagrams? (You probably realized I was just using powerpoint)
  #4   Spotlight this post!  
Unread 01-11-2012, 08:24 PM
Ether's Avatar
Ether Ether is offline
systems engineer (retired)
no team
 
Join Date: Nov 2009
Rookie Year: 1969
Location: US
Posts: 6,107
Ether has a reputation beyond reputeEther has a reputation beyond reputeEther has a reputation beyond reputeEther has a reputation beyond reputeEther has a reputation beyond reputeEther has a reputation beyond reputeEther has a reputation beyond reputeEther has a reputation beyond reputeEther has a reputation beyond reputeEther has a reputation beyond reputeEther has a reputation beyond repute
Re: The physics of flipping

Quote:
Originally Posted by lemiant View Post
Do you know what would be a reasonable estimate for the max acceleration of an average robot (12fps top speed, 6wd traction wheels, CIMple gearboxes, 4 CIMs)?
Use JVN's mechanical calculator, located here.


Quote:
PS What do you use to make those pretty diagrams? (You probably realized I was just using powerpoint)
That one was also Powerpoint.
  #5   Spotlight this post!  
Unread 01-11-2012, 08:56 PM
lemiant's Avatar
lemiant lemiant is offline
the Dreamer
AKA: Alex
FRC #4334 (Alberta Tech Alliance)
Team Role: Leadership
 
Join Date: Feb 2009
Rookie Year: 2008
Location: Calgary, AB, Canada
Posts: 553
lemiant has a reputation beyond reputelemiant has a reputation beyond reputelemiant has a reputation beyond reputelemiant has a reputation beyond reputelemiant has a reputation beyond reputelemiant has a reputation beyond reputelemiant has a reputation beyond reputelemiant has a reputation beyond reputelemiant has a reputation beyond reputelemiant has a reputation beyond reputelemiant has a reputation beyond repute
Re: The physics of flipping

Quote:
Originally Posted by Ether View Post
Use JVN's mechanical calculator, located here.
I haven't used JVN's calculator in a while, but I' don't think it gives acceleration.

On the other hand I plugged this into wolfram alpha (so I don't have to worry about all that unit conversion):

(21 in-lb / ((12fps / 5310 rpm) / (2*pi (inches/revolution)/inch)))/120lb to m/s^2 * 80%

Getting a max acceleration for my previously stated bot of 5.3 m/s^2. This is approximately half the force of gravity.
Based off that we can have a center of gravity at most ~2x as high as it is far from the front/back of the wheel base (whichever is closer), before you will flip due to accelerating on a flat field.
I would probably suggest keeping it below 1.5x though, for safety.
Quote:
e.x. 37" long robot with a center of mass that is nearly centered on the robot has the following characteristics:
Wheel base = 37 - 2*4
= 37 - 8
= 29"

CoM to edge of wheelbase = 29/2
= 14.5"

Max height of CoM = 1.5 * 14.5"
= ~22"
I ball-parked pretty much every number in this math but it does tell us one thing:
Quote:
If your long-orientation robot has a CoM more than 22" off the ground (or 14" for a wide-bot), you'd better think twice and prototype 10x, because you're in the danger zone!!! NOTE, this doesn't mean that less than those thresholds is safe, it's just that over them is super risky.
Ether, did I overlook anything? If this is reasonably representative for most teams then I'll move it to the top, and hope it helps some people.
  #6   Spotlight this post!  
Unread 01-11-2012, 09:06 PM
DonRotolo's Avatar
DonRotolo DonRotolo is offline
Feeling Honorable
FRC #1676 (Pascack PI Oneers)
Team Role: Mentor
 
Join Date: Jan 2005
Rookie Year: 2005
Location: Montvale NJ
Posts: 6,444
DonRotolo has a reputation beyond reputeDonRotolo has a reputation beyond reputeDonRotolo has a reputation beyond reputeDonRotolo has a reputation beyond reputeDonRotolo has a reputation beyond reputeDonRotolo has a reputation beyond reputeDonRotolo has a reputation beyond reputeDonRotolo has a reputation beyond reputeDonRotolo has a reputation beyond reputeDonRotolo has a reputation beyond reputeDonRotolo has a reputation beyond repute
Re: The physics of flipping

Quote:
Originally Posted by lemiant View Post
Do you know what would be a reasonable estimate for the max acceleration of an average robot (12fps top speed, 6wd traction wheels, CIMple gearboxes, 4 CIMs)?
I can't hazard a guess, but I'm more worried about acceleration with a minus sign - like when I am moving at 12 fps and stop dead when I hit the bump. If F=Ma, and a is going from 12 to zero in an umptosecond, F is going to have some serious magnitude regardless of M.

I am seriously working to get our CoM below 6 inches.
__________________

I am N2IRZ - What's your callsign?
  #7   Spotlight this post!  
Unread 01-11-2012, 09:50 PM
Ether's Avatar
Ether Ether is offline
systems engineer (retired)
no team
 
Join Date: Nov 2009
Rookie Year: 1969
Location: US
Posts: 6,107
Ether has a reputation beyond reputeEther has a reputation beyond reputeEther has a reputation beyond reputeEther has a reputation beyond reputeEther has a reputation beyond reputeEther has a reputation beyond reputeEther has a reputation beyond reputeEther has a reputation beyond reputeEther has a reputation beyond reputeEther has a reputation beyond reputeEther has a reputation beyond repute
Re: The physics of flipping

Quote:
Originally Posted by lemiant View Post
did I overlook anything?
Yes, what Don said:

Quote:
Originally Posted by DonRotolo View Post
I'm more worried about acceleration with a minus sign - like when I am moving at 12 fps and stop dead when I hit the bump. If F=Ma, and a is going from 12 to zero in an umptosecond, F is going to have some serious magnitude

  #8   Spotlight this post!  
Unread 01-11-2012, 11:56 PM
ewhitman ewhitman is offline
Registered User
FRC #3504 (Girls of Steel)
Team Role: Mentor
 
Join Date: Jun 2011
Rookie Year: 2004
Location: Carnegie Mellon University
Posts: 12
ewhitman is an unknown quantity at this point
Re: The physics of flipping

This problem can be addressed by the concept of the Zero Moment Point. The ZMP is most often used in the context of determining tipping for humanoid robots, but it applies here.

The ZMP is the point on the ground through which a single force would act to achieve a given Center of Mass acceleration without any change in angular momentum.

If the ZMP leaves your wheel base (convex hull of your points of support), your robot will begin to tip.

The relevant formula is: Z = -h/g*a

where:
Z = the location of the ZMP relative to the CoM (in m)
h = the height of the CoM (in m)
g = the acceleration due to gravity (9.8 m/s/s)
a = the acceleration of the CoM (in m/s/s)

This means that while sitting still or traveling at a constant speed (a = 0), the ZMP is directly under the CoM (Z=0), which is hopefully inside your wheel base.

However, if your CoM is 50 cm high, and you accelerate forward at 5 m/s/s, your ZMP will move backwards 25.5 cm. (0.255 = -0.5/9.8*5) If your CoM is less than 25.5 cm in front of your rear wheels, you will begin to tip because the ZMP will have left your wheel base.

If I haven't explained the math well enough, the moral is:
1) Keep your CoM low
2) Keep your wheel base big and your CoM near the center of it
__________________
2004 - student 1257
2005 - mentor 1257
2006 - mentor 1257
2011 - mentor 3504
2012 - mentor 3504
2013 - mentor 3504
  #9   Spotlight this post!  
Unread 01-12-2012, 01:43 AM
compwiztobe's Avatar
compwiztobe compwiztobe is offline
Always Aspiring
AKA: Aren Siekmeier
FRC #2175 (The Fighting Calculators)
Team Role: Mentor
 
Join Date: Apr 2008
Rookie Year: 2008
Location: Woodbury, MN
Posts: 591
compwiztobe has a reputation beyond reputecompwiztobe has a reputation beyond reputecompwiztobe has a reputation beyond reputecompwiztobe has a reputation beyond reputecompwiztobe has a reputation beyond reputecompwiztobe has a reputation beyond reputecompwiztobe has a reputation beyond reputecompwiztobe has a reputation beyond reputecompwiztobe has a reputation beyond reputecompwiztobe has a reputation beyond reputecompwiztobe has a reputation beyond repute
Re: The physics of flipping

The negative acceleration pointed out by Don is definitely the one we're worried about too. We're trying to keep the angle between the floor and the line between our rear contact and the CG less than 45 degrees so that we can experience as much as 1g laterally and be just fine. And even lower is even better. This includes when we are crossing the bump/bridge, so depending on wheel profile, the angle on flat ground needs to be potentially as small as 22 degrees, making a short wheel base harder and harder.
  #10   Spotlight this post!  
Unread 01-12-2012, 05:58 AM
PayneTrain's Avatar
PayneTrain PayneTrain is offline
Unprepared
AKA: Wil Payne (@Wil_Payne)
FRC #0422 (The Mech Tech Dragons)
Team Role: Mentor
 
Join Date: Mar 2010
Rookie Year: 2008
Location: RVA
Posts: 1,230
PayneTrain has a reputation beyond reputePayneTrain has a reputation beyond reputePayneTrain has a reputation beyond reputePayneTrain has a reputation beyond reputePayneTrain has a reputation beyond reputePayneTrain has a reputation beyond reputePayneTrain has a reputation beyond reputePayneTrain has a reputation beyond reputePayneTrain has a reputation beyond reputePayneTrain has a reputation beyond reputePayneTrain has a reputation beyond repute
Send a message via Skype™ to PayneTrain
Re: The physics of flipping

Quote:
Originally Posted by DonRotolo View Post
I can't hazard a guess, but I'm more worried about acceleration with a minus sign - like when I am moving at 12 fps and stop dead when I hit the bump. If F=Ma, and a is going from 12 to zero in an umptosecond, F is going to have some serious magnitude regardless of M.

I am seriously working to get our CoM below 6 inches.
I'm curious to see how much robot you're going to fit in such a small space. I think we're aiming for about 8-12 inches. Given the posts I have seen on CD, I assume your team is using a narrow intake, which probably helps a lot when trying to acheive a low COM.
__________________
Don't follow your dreams; follow my Twitter!
  #11   Spotlight this post!  
Unread 01-12-2012, 06:50 AM
IKE's Avatar
IKE IKE is offline
FF Pure Mi
AKA: Isaac Rife
no team (N/A)
Team Role: Mechanical
 
Join Date: Jan 2008
Rookie Year: 2003
Location: Michigan
Posts: 1,769
IKE has a reputation beyond reputeIKE has a reputation beyond reputeIKE has a reputation beyond reputeIKE has a reputation beyond reputeIKE has a reputation beyond reputeIKE has a reputation beyond reputeIKE has a reputation beyond reputeIKE has a reputation beyond reputeIKE has a reputation beyond reputeIKE has a reputation beyond reputeIKE has a reputation beyond repute
Re: The physics of flipping

Some other factors to take into consideration:

Torque at the wheel. Larger torque on the rear wheels also adds to the moment of tipping. For the same traction force and acceleration, the larger the rear wheel will require larger torque and thus be more prone to tipping (works both ways including dynamic braking).

Another big factor is if you plan to go on the ramp. As you climb the incline, the normal force on the rear wheels will increase and thus have a higher traction potential. If you then apply a large torque to accelerate up the ramp, you can flip over as well. Tilt your Powerpoint model 15 degrees, and you will see how the gravity vector will now angle more rearward. http://www.chiefdelphi.com/media/papers/2321

Last but certainly not least, wheel and carpet compliance can be very big in flipping. The compliance in the carpet and your wheels/tires can act as a spring. When timed wrong, shifting back and forth can exercise those springs. The more compliant the wheel/tire (pneumatic), the more effect you can get. This can start to get complicated pretty quick.

A good "rule of thumb" for a drivetrain that you plan on having traction limited (gearing and motors powerful enough to spin the tires) is...
Assuming a Coefficient of friction of 1, then the acceleration and traction vector can be equal, and thus your CG needs to fall inside of 45 degree lines from your tire contact patches. Higher COF means a lower angle (though not much lower). Wanting to traverse inclines means reducing angle as well. Assuming the 15 degree ramp is a goal, keeping your CG below 30 degree lines should be fairly conservative. For a long robot with 8" wheels ((38-8)/2/sqrt(3)=8.67), this would be keeping the CG in the center below 9" and lower the more offset from center it becomes. For a wide bot with 8" wheels (((28-8)/2/sqrt(3)=5.78), would be keeping the CG lower than 6" (which can be tough with 8" wheels)...
  #12   Spotlight this post!  
Unread 01-12-2012, 04:26 PM
SteveJanesch SteveJanesch is offline
hopes he has enough oomph
FRC #1533 (Triple Strange)
Team Role: Mentor
 
Join Date: Apr 2007
Rookie Year: 2006
Location: Greensboro, NC
Posts: 103
SteveJanesch is a splendid one to beholdSteveJanesch is a splendid one to beholdSteveJanesch is a splendid one to beholdSteveJanesch is a splendid one to beholdSteveJanesch is a splendid one to beholdSteveJanesch is a splendid one to beholdSteveJanesch is a splendid one to behold
Re: The physics of flipping

At the risk of telling you something you already know...
It's not just acceleration that causes tipping - it's the fact that the accelerating force is applied away from the center of gravity (by the wheels, on the floor) that imparts the torque around the COG that can tip the robot. If your accelerating force were applied parallel to the floor and at the same height as the COG there'd be no torque to cause the tipping (ignoring friction, of course).

Great question, Alex, thanks for posting it. And great responses, too.

- Steve
  #13   Spotlight this post!  
Unread 01-17-2012, 11:25 AM
Ether's Avatar
Ether Ether is offline
systems engineer (retired)
no team
 
Join Date: Nov 2009
Rookie Year: 1969
Location: US
Posts: 6,107
Ether has a reputation beyond reputeEther has a reputation beyond reputeEther has a reputation beyond reputeEther has a reputation beyond reputeEther has a reputation beyond reputeEther has a reputation beyond reputeEther has a reputation beyond reputeEther has a reputation beyond reputeEther has a reputation beyond reputeEther has a reputation beyond reputeEther has a reputation beyond repute
Re: The physics of flipping

Quote:
Originally Posted by IKE View Post
Some other factors to take into consideration:

Torque at the wheel. Larger torque on the rear wheels also adds to the moment of tipping. For the same traction force and acceleration, the larger the rear wheel will require larger torque and thus be more prone to tipping
I've been meaning to come back to this.

If the ratio of the vehicle mass to the mass of the rear wheels is sufficiently greater than (1+2*r/h), then the radius drops out of the formula for tipping acceleration, and the result is the formula posted earlier in this thread.

See attachment.

Attached Files
File Type: pdf flip bot solution.pdf (14.5 KB, 46 views)
Closed Thread


Thread Tools
Display Modes Rate This Thread
Rate This Thread:

Posting Rules
You may not post new threads
You may not post replies
You may not post attachments
You may not edit your posts

vB code is On
Smilies are On
[IMG] code is On
HTML code is Off
Forum Jump


All times are GMT -5. The time now is 11:53 AM.

The Chief Delphi Forums are sponsored by Innovation First International, Inc.


Powered by vBulletin® Version 3.6.4
Copyright ©2000 - 2014, Jelsoft Enterprises Ltd.
Copyright © Chief Delphi