Well, assuming you want to power all of the wheels, the forces generated by mecanum wheels has been discussed extensively. Similar analysis can be done for any combination and configuration of wheels.
For example, if using vector analysis on a 4-wheel partial mecanum drive:
-Two of the wheels can be modeled as described in the second linked pdf
-The other two will provide propulsive force only in the front-to-back direction. The ‘only’ side-to-side force will be friction, which will be whatever is needed to negate any forces acting on the wheel in that direction, up to the point where static friction is overcome.*
(*This is, of course, an approximation, YMMV)
I’m interested in how it would work. I put that wheel layout on a VEX square bot frame. I programmed it to be a regular Mecanum layout and it doesn’t work well. Forward reverse works, but turning has the rear scrubbing.
The single rear omni is interesting since that would help the turning issues, and while moving forward the rollers would work well.
So with my little build failing with what could be the wrong code, I thought I’d try some math, hence the search here.
5132’s bot this year was a 4 wheel drivetrain with independent suspension. It had 10" Pneumatic wheels in front to take the abuse and 8" Mecanums in the rear to reduce scrub and assist in maneuverability. It works pretty well, but if the mecanums are on the wrong sides, it made a huge difference, as the lateral forces of the wheels are fighting each other. I believe our students also programmed it as a standard tank drive, not mecanum drive. Mecanum drive doesn’t seem like it would provide the correct directional commands to give you the driving you are looking for.
1: Change programming to tank drive, and test.
2: If that didn’t fix the driving, flip your left and right mecanums.
This design is not going to strafe, no matter how you turn the wheels, barring some unusual anisotropic coefficients of friction.
Placed on an approximately square base, this design would be marginally better at turning and marginally worse at driving directly forward than using omnis in the rear and using tank drive (that is, linking the front and rear wheels on each side).
Without strafe capability, I don’t see an advantage that justifies the two extra drive trains.
A tricycle layout might be interesting. you could drive the rear wheels and pivot on the front wheel. If you replaced the front wheel with a single swerve module, then you restore the holonomic drive capability. The fact that there are three points of contact eliminates the need for suspension in most cases.
I do agree that this chassis should be driven as tank drive - and that it can not strafe. The tank drive can (should) use one gearbox per side and as always all wheels should be driven.
I have not tried it, but I would imagine it would behave better than traction and omni. Assuming the same rubber on omni and mecanum, it should have comparable COF and perform nearly identical forward, backwards. Turning should be better with mecanum - but more importantly, the resistance to being spun by a defender should be much better. In the past, we did not try this configuration given the size and weight (and cost) difference between omni and mecanum. Now, with the modern VEX mecanum, I believe it is worth another look.