Here’s a few thoughts…

(1) Although this first thought doesn’t solve the problem its worth mentioning I think. It does look like a design flaw with the open sides on the wheels, especially in that very dusty looking ground, although thats obviously easier to say in hindsight, that isn’t my point, as I’m not trying to be critical. I see it as just simply highlighting a different wheel design may well be needed in future rovers?

(2) Why does it look like (in that other link) that they are trying to go up hill at all?. Why not just aim to go down hill, as then gravity helps, until its freed itself from the dust in the wheels, then drive around and then try another route out if they really want to go up hill.

To do that, it would be like moving crab like down the hill via turning on the spot until the left free wheels were lower than both trapped right wheels, then go back and forth, with the left free wheels about +/- one half length of the rover, which would drag the upper wheels out and down the hill slightly in a zig-zag. (It would dig the trapped wheels in during part of the turn, (especially due to the open design of the wheels) but as the rover turned it would partly free the trapped wheels again as they turned partly side ways again to the slope of the hill. At some point it should drag the trapped wheels free enough to make another attempt to completely or even partly turn the trapped wheels, to try to make a break for it down hill, to clear out the wheels and then focus on finding somewhere quick to stop and get some more solar power.

(I guess they have built a simulation of the hill to try out experiments here on Earth, so its worth giving it a try with a test rover, if they haven’t tried this crab like movement yet).

Just a thought. Its better to try, than get stuck with no power.

You’ve already covered my thoughts in 2
I hope they’ve been trying to go downhill as any attempt to continue up would be futile. You would think that somebody in the control room at nasa would know something about driving an offroad vehicle.
As for the wheel design if they could make inflating/deflating tyres it may help as any good four wheel driver knows when the sand gets soft deflate your tyres.

The reason they didn’t use inflatable tires is that it is very cold and most substances are hard at that temp and the possibility of deflation is to risky. Also the soil is abrasive so durability needs to be high.

My guess to why there is an open wheel design is to firstly allow the wheel to flex a little. Also the wheels have a motor within each hub so you need room to have the arm/motor. Also the wheel has one portion that is an open grate i would believe it is to allow the particles to exit the wheel and maybe to also dig in a little in some situations. Remember this vehicle is moving at extremely slow speeds compared to a normal earth vehicle so it has little movement to dislodge accumulated dirt. I wonder if there is some better wheel designs like the twheel that have more give. However that probably wouldnt help as it just needs more traction so it needs wider tires and with that you need more space to launch and to move around on mars.

Spirit’s plight proves the vulnerability of wheeled vehicles on a sandy, rubbled surface. Tracked vehicles would be far more reliable and future rovers should employ tracked systems. The current pair use six wheels and this method, as I understand it, was selected in order to save space and weight. Larger vehicles can and should be designed and deployed to continue surface exploration of the planet. I echo the numerous comments complimenting this very fine article. The more people who participate, even the nay-sayers, the more likely it is that a manned Mars mission will become a reality.