Calculate Speed of a Non Standard X Drive

[technik3k]

@Xenon27, I think you will find these two discussions informative and interesting:

@technik3k

There was recently a very interesting thread on Chief Delphi where they discussed pros and cons of the Mecanum vs X-Drive (which they call Poor Man’s Mecanum or PMM).

This post by GeeTwo describes an asymmetric X-Drive:

Chief Delphi – 20 Jun 19

Mecanum vs Poor Man’s Mecanum

Another difference which has not been noted here between Mecanum and what OP refers to as PMM: With the same motors, gearing, and wheel size, Mecanum accelerates 41% better than PMM, while PMM has a 41% higher free speed than Mecanum. The big…

A wrinkle on PMM I experimented with a couple of years ago is one I called Pakuni Drive†, named after the simian aliens from Land of the Lost and their attribute of walking forwards like humans, but running sideways like my little brother Vernon when he was 18 months old. The idea is that I toed in the wheels ~22.5° rather than 45°. (It turns out that the acute angle on a 5-12-13 right triangle is closer to 22.62°, so that’s what I really did.) Anyway, this gives a forward acceleration which is 2.4x better in the forward direction than the lateral (strafe) direction, but a free speed which is 2.4x better in the lateral. My intention was to start the robot accelerating in the “forward” direction, then rotate the robot 90 degrees to “shift” to a speed 2.4x as fast for longer (cross-field) runs. My attempts with an arduino and no gyro or other feedback nor radio input were unsuccessful, so I’m putting the concept out there in case anyone wants to try this with better control systems.

† My earlier name for this before inspiration hit was roto-shifter, as will be explained in later sentences.

@technik3k

In addition to video link in OP, anybody interested in this topic may want to check AURA’s experiment video as well as their tutorials.

To answer the question about torques, here is the graph of the force and velocity as the function of x = angle between proposed wheel orientation and the default orientation as in the tank drive (straight forward):

The unit of force is a single motor max (stalling) output and the unit of velocity is similarly its max (idle) velocity. In case when x=0 (tank drive) the force is 2 (two motors) and velocity is 1. Then, in the ideal case, force will drop as the function of cos(x) and velocity will grow reciprocally (dashed lines).

However, in the real world, friction, especially in the omni rollers, will make things less than ideal. As the angle (x) increases so will the friction loses and both force and velocity will start underperforming their ideal curves more and more (solid lines on the graph). Real formulas would be more complicated and I made friction coefficient high for the illustration purposes, but at some angle (x) the wheels will either slip or the friction will be consuming almost all available motor power, PTCs will be tripping, and both velocity and torque will effectively go to zero.

Note that power curves are not the real power output of the motors, since you cannot have both max torque and max velocity at the same time. Still they are useful for comparison of what you could expect from your setup.

So to answer original question I would agree with @Cody and recommend against 30 / 60 degree drive, because at higher angles it will be more sensitive to extra friction and you will be losing power fast.

But it would make a great entry for the eng. notebook to build a test chassis and measure actual forces you could get out of it. And, if you like what you get, it may work great for you.