Some of you may have already seen the inevitable, horrible conclusion. Yes, that's right, it's the POGO UNICYCLE. Instead of a seat, the pogo unicycle has a pogo-type assembly, sans spring. Both cranks on the wheel are turned in the same direction, and both of them are attached via fixed-length bars with pivots on either end to the bottom of the pogo mechanism, resulting in the standard mechanism for converting circular to reciprocating motion. It should be a fairly simple device to build (although note that it's important for the pogo assembly to not allow the handlebars to rotate relative to the base, unlike in normal pogo sticks).
The physics of the pogo unicycle are fairly interesting. The length of the cranks should be such that the distance the user bounces up and down should be about the distance they do on a pogo stick. The diameter of the wheel should be such that if the user is bouncing up and down at about the rate they do on a pogo stick then the amount of upward force on the bounce up is about the same as it is on a pogo stick. I don't have available numbers or formulas to calculate these things, if someone can supply them I'd much appreciate it. In particular, I'd like to know what the natural rate of moving forward on a pogo unicycle is.
Other than a bit of clunkiness caused by the obvious discontinuity of movement, the pogo unicycle should be about as efficient to ride and maneuverable as a regular unicycle. Whether it would be harder or easier to ride is highly unclear, one would really have to build one and try it to find out. It would undoubtedly attract a lot of attention riding down the street.
A less wacky vehicle which I also came up with cogitating on my last post is to make a step-machine bicycle. Simply put a step machine assembly on a bicycle (really just two steps pivoting about the same point in the front) and attach them to corresponding pedals via fixed-length bars which pivot on either end, again building the standard circular to reciprocating motion assembly.
In theory it may be possible for such a setup to have greater efficiency than regular bike pedals, but experiments trying to do that with oval-shaped pedal motions appear to have been a failure, and aerodynamics are inevitably going to suck because, duh, you're standing. I'm more interested in it simply to have the ergonomics of a step machine in a bicycle, and also to be just plain weird.
Step machine is just one of several different ergonomic interfaces for powering a bicycle. Several others which have already been tried are rowing, walking, and, uh, pedalling.
There's also the obvious pushing. Their web site says that real wheels make the bike much faster than those dinky little two-wheel scooters which are so ubiquitous these days (and were ubiquitous back in the 50's, or so, then went completely out of style). I'm not clear on why bigger wheels should be faster other than that there's less friction, and obviously they're way more stable and turn better.
I have a little confession to make about manual scooters. I had a really bad wipe-out on one a few years ago. You see, I bought a super-cheap knockoff on clearance for about $15. It was really cheap and the handlebars wouldn't tighten to a specific height, but they could still be used to turn, so whatever. I practiced riding it back and forth in my apartment, which basically meant doing a single push-off and gliding across the whole place, since I had a flat floor and a tiny San Francisco apartment. After I got pretty good at that, I tried riding it on the street. The first thing I noticed was that shifting weight from the ground to the scooter isn't completely trivial, and I was quite awkward my first day riding it. My second day went quite a bit more smoothly. I was also working on downhill, taking it carefully and sticking strictly to speeds I could handle. Apparently my skill at that was also going up pretty quickly, because (for those of you who know San Francisco) I was going down Bush street at the end of the second day. That wouldn't have been all that bad, except I was going down Bush street without using the brakes at all. I did notice that people were getting way out of my way, even when I wouldn't have come anywhere near hitting them had they stayed put.
Towards the end of my second day of riding, I was riding down the street in Oakland at night, kind of zoning out because riding wasn't requiring much thought, when I went over a section of street with an enormous number of cracks which was in shadow so I couldn't see it at all. Suddenly the handlebars pulled very strongly to the right - my guess is that the front wheel hit a crack with its left side only, causing the whole scooter to precess and pulling the bars away from me. I flew off the thing, and managed to roll on the ground in lieu of hitting it directly and getting a concussion (a little trick I learned the last time I wiped out, that time doing something even stupider). In the process I injured the ball of my right foot (because it was standing on the scooter - to have been injured that way I must have been going at a pretty good clip) plus skimmed my right knee, my right wrist, my right elbow, and seriously hurt my left wrist, my left shoulder (rolled on it) my left elbow, and got the wind completely knocked out of me.
At first I was most worried about my left shoulder, because that hurt a lot. After a few minutes I regained the ability to breathe, and rode the rest of the way home (I'd moved to Oakland by this time, hence the jump from San Francisco). By the time I got home I couldn't lift my keys with my left hand, because my left elbow had become non-functional. After about an hour my elbow was in excruciating pain, which it remained in for the next week, at which point it only hurt when it moved more than a millimeter off a 90 degree angle. It was months before I could straighten my left arm out completely, even after the pain had stopped. (Note to self: the next time you roll, hit the ground with the back rather than the front of your hand.)
The moral of this story could be to wear a helmet, knee, and elbow pads, although the more direct conclusions are that you should learn to roll well before riding in anything, and you shouldn't ride on vehicles which are practically designed to wipe out if you hit a crack in the sidewalk. All of which is my long-winded way of saying that small-wheeled manual scooters are an awful design of vehicle, and the big-wheeled kick scooters are probably vastly better.