pic: OmniSwerve chassis Bottom View and Concept Discussion

[asid61]

Originally Posted by GeeTwo

The velocity vectors can add up so that the speed of the robot is greater than the speed that any individual wheel is driven. The issue is that with the number of rollers providing resistance to this motion, I find it unlikely that those two motors could achieve a significantly greater speed than one in which all three motors are providing drive force in the desired direction. The only way to know for sure is to build it.

Well, if you take the two non-pointing-in-the-right-direction motors and give them each an angle theta away from the main wheel...
If you assume velocity vectors add, then the output speed is (cos(theta)+1)*v0, right? If that's the case, as theta goes to 0* (AKA point all whee;s in the same direction) one would end up with just 2 times the target speed- but all the wheels are just pointing in the same direction like a tank drive. That doesn't make sense to me, is there another way to add it?

[Aren Siekmeier]

Force vectors add. Velocity vectors do not. Rather they are constrained by slip conditions and the relative motion of bodies.

It's sort of a continuously variable transmission.

Say you are constrained to go in a direction 0 (by a wall or omnis opposing each other, etc.), but an omni wheel is pointed in a direction theta relative to your heading, and spinning at speed w about its axis. The overall translation velocity vector v is identically the velocity of the center of the wheel relative to the ground, which can be broken into the rotation of the wheel (w), and the rotation of the rollers (s), assuming no slippage. Then v must project onto the wheel speed w, as w=v*cos(theta). The roller speed is s=v*sin(theta) and has no limit. The overall speed is v = w/cos(theta), resulting in a higher speed.

To do this, you could have a four wheel drive with steerable omnis in each corner. Start with them directed forward, (theta=0), and spin the wheels at speed w. Then v = w / cos(0) = w. Then turn the left and right wheels toward the middle by an angle theta. Now v = w / cos(theta) will give an increase in top speed.

However, the force available in the forward direction drops. Each wheel supplies F in its own direction. When theta = 0 then the total force is 4*F, all straight forward with no sideways component. When theta is increased, the sideways components cancel, but at each wheel, the sideways component must add with the forward component to get F in the direction theta. So the forward component from each wheel is F*cos(theta), and the overall force available is 4F*cos(theta).

In this way, steering the wheels toward the middle by an angle theta acts as another stage of reduction, increasing the speed and decreasing the force by a factor of cos(theta), assuming no wheel slippage.

Vector diagram to help