Circling Bodies

First — don't be shy — try a few motions with your own body. Twist an extended arm as far as you can one way and then twist it the other way. Your wrist (mainly) can't even do a full 360-degree rotation. Twist your neck — your head won't rotate even as far as your hand did. Your lower back's mobility limits how far your torso can rotate just as severely, and feet (mainly ankles) feel still greater rotational constraint. All sorts of limbering and muscle-strengthening exercises depend on rotation — "curls" just put the matter more explicitly. After all, appendages hook on to us at pivot points around which they swing. But they swing through limited arcs, with varying degrees of constraint. Thus arms move around shoulders more freely; legs around hips less so, with flexibility evidently traded against stability and reliability. No picture need be provided; doing it yourself should be persuasive.

Continuous rotation, as with a proper wheel? For better or worse, no animal joint has ever managed that trick. Yes, we humans can rotate continuously — but only if we do it as a whole-body activity — as do somersaulting or rolling children. Almost all other creatures that rotate live within that general limitation as well. We're looking at tumbleweeds, a shrimp that rolls back to the water when washed up on a beach, a caterpillar that rotates head over heels, so to speak, and the helicopter-like seeds (really fruits, technically samaras) of trees such as maples. More about these systems in a few pages.

Then look around. Sure, we've created a host of devices that may turn but also face (by design) much the same limitation on rotation — most hinges, door handles, light switches, latches, staplers, scissors, pliers ... But playing a far more central role in our technology are things that rotate without limit as parts of otherwise non-turners, things that go around and around as long as they're driven and perhaps a little longer. I mean devices based on that marvelous invention, the wheel and axle. That includes almost all of our motors and their associated shafts, pulleys, gears, and so forth. It includes our diverse wheeled and propeller-driven vehicles. Plus all manner of hand tools, from eggbeaters to socket wrenches. Long ago that meant wagons and potter's wheels, and the diversity of our rotational contraptions has been on the increase throughout our history. No doubt at all — mechanisms that rotate as parts of otherwise non-rotating contrivances form the very core of our mechanical technology.

We thus glimpse a paradoxical problem. Through most of human history (and prehistory, if you prefer the distinction), muscle has been the main motor of our technology, whether we work our own personal meat or persuade that of our domesticated animals to do our jobs. Muscle can only pull, and it must remain attached at both its ends. How can a non-rotating engine drive truly rotational machinery? This book explores the diverse ways that humans have faced up to and managed to deal with that most basic of dilemmas. In essence, it explores one facet of the biomechanics behind history.

Your immediate rejoinder might be that the difficulty yields to a trivially simple fix. Specifically, just add a crank, a lever extending radially outward from the rotating shaft with a slip fitting on a sideways extension of that lever. No need for an illustration — we make such things all the time, from hand-operated household gear such as pencil sharpeners, eggbeaters, and meat grinders to the engines of our cars, in which pistons moving (for most cars) up and down crank and thereby turn drive shafts. That slip fitting might be nothing more than a greasy hand or a loosely fitting outer handle of wood or plastic. It seems reasonable that this obvious trick should have been particularly appropriate for ancient devices, with their slow rotation rates. Oddly enough, cranks remained unknown (or nearly so) until about a thousand years ago. Think of it — for all their sophistication, the classical Mediterranean civilizations made no significant use of this simple and now ubiquitous arrangement. Punning subtly, one might ask, where's the rub?

Muscle-powered rotational machinery obviously has a much longer history than cranks — think again about all those wagons, chariots, and potter's wheels. How, then, were they persuaded to rotate? And have these more ancient fixes persisted, even gained in importance, with the further proliferation of rotational devices? No surprise — one question leads to another.

First, then, what are the options for making shafts and wheels turn? If nothing else, its peculiar modernity tells us that a crank isn't the only thing that will work. Consider some other possibilities, put as a series that I don't assert is chronological, fully complete, or mutually exclusive — and at the expense of suspense ...

• Roll the top of a cylinder by pushing something across it while the bottom then rolls (at half the speed) along the ground — rolling a log or barrel, as in figure 1.1. Of course, sooner or later (more likely sooner), the propelling roller on top leaves the driven roller behind. So you can't cover much distance without fairly often moving the roller left behind from rear to front. Even with a series of driven rollers, creating a new front one with a rear reject remains required. The simpler French-style or rod-type rolling pin works this way; its task doesn't ask that it roll very far and allows easy lifting and repositioning

• Pull or push on the axis of a wheel while a part of its circumference contacts the ground with enough friction so it rotates rather than just sliding along — as a horse pulls a cart and as in figure 1.2; or as you use a conventional rolling pin, one with a rotating handle at each end, by pushing or pulling the handles. The rolling pin then rotates as it presses the pie crust, although the handles do not. Proper bearings aren't absolutely necessary — a person can pull along a bagel-shaped (toroidal) water tank, hauling on a rope that loops through its center hole.

• Make an animal (perhaps a person) walk while pushing or pulling in monotonous circles around a vertical shaft or drum from which a radial lever protrudes — for example, turning a large posthole digger (auger), as in figure 1.3. The motor itself then rotates at just the same speed as the shaft or drum, so no bearing need be supplied — at least between the two. (Of course, that shaft or drum will typically turn around its own bearing.) Years ago, playgrounds had small merry-go-rounds driven by one or more children as others sat on the deck and made encouraging noises.

• Grab the handle of a tool, turn it through an arc, then release it, grab it again after turning one's arm or body some ways opposite the direction of the tool's rotation, and turn it again, as in figure...