pic: 2826 Halonomic Drive Prototype

[EricH]

Originally Posted by Jared341

I think you have that backwards - an O pattern on the ground provides more efficient turning. In fact, I don't believe that a square robot with an X on the ground can turn at all.

To turn clockwise with an O pattern on the ground (or an X pattern looking at the top of the robot):
The front left wheel provides equal torque in the FORWARD and RIGHT directions.
The front right wheel provides equal torque in the BACKWARD and RIGHT directions.
The rear left wheel provides equal torque in the FORWARD and LEFT directions.
The rear right wheel provides equal torque in the BACKWARD and LEFT directions.

Hence 100% of the torque (for a square robot) is around the axis of rotation. For an elongated drive base with 45 degree offset rollers, the percentage is less than 100%.

Now consider a clockwise turn for the opposite configuration - X on the ground (looks like an O looking at the top of the robot): None of the four wheels can supply torque around the axis of rotation (only towards or away from it). For a non-square drive base this isn't the case, but the percentage of output torque that aids in rotation is still going to be less than 100%.

* All of this assumes 45 degree offset rollers with negligible friction. If the rollers are sufficiently sticky, you can achieve an increased turning effect with the X on the ground (at the cost of decreased strafing efficiency).

Are you sure about that torque pattern? You may be mistaking the contact pattern for the vector pattern.

Clockwise, O contact pattern on the ground, lines are vectors in a clockwise turn, arrows are vertical component of the vector:

\../ (^v)
/..\ (^v)

Clockwise, X contact pattern on the ground, lines are vectors in a clockwise turn, arrows are vertical component of the vector:

/..\ (^v)
\../ (^v)

So, the X pattern forms a circle on the ground with its force, while the O forms an x pattern for the same turn. Note that all vectors are in the direction perpendicular to the rollers for that wheel. If you have an O pattern, perfect square, the vectors go into the middle. An X pattern will go around the center.

Note that ALL patterns I reference are in relation to the ground contact. I don't care about what the pattern is off the ground.

Alan, the reason you may notice an O pattern turning better would probably be that the rollers are forced into the sides of the wheel, locking them temporarily, while an X pattern is easily spun due to the rollers not going into the sides. Assuming that the rollers were to stay in the center on all wheels (i.e., no friction with the sides of the wheel), I'm not sure that you'd see the same effect.

Again, if you don't like the results one way, swap end-to-end, side-to-side, or (in this case) top-to-bottom and see if you like those results better.