4Joints: the ones that turn and the ones that slide

Open a door and watch the edge of it. Every point on the door moves along a circle, and the circle's center is the line running through the hinges. Now pull a drawer out. Every point on the drawer moves along a straight line, and none of it turns at all. Almost every robot is made of doors and drawers. This module is about telling them apart, finding where each one stops, and seeing why the door wins.

A hinge is a joint that lets two links, the rigid pieces on either side of it, turn around one line and do nothing else. Your elbow, a door and a wheel on its axle are all hinges. Engineers call that line its axis, and the joint a revolute joint. Where a hinge is takes one number, and that number is an angle: how far it has turned from where it started.

A slide joint is a joint that lets two links slide along one line and do nothing else. A drawer is one, and so is the lift on a forklift. Engineers call it a prismatic joint. Where a slide joint is also takes one number, but the number is a distance: how far it has moved along the line.

Each is one degree of freedom. The difference is the kind of number: an angle for a hinge, a distance for a slide joint.

Try it on five joints

The box below holds five joints, each on its own pedestal with its own slider, attached to nothing else. From left to right: a plain hinge, a slide, a hinge with limits, a ball joint, and two hinges joined in a chain. The label over each pedestal says which is which. Every slider has a readout next to it: the slider is what you are asking for, and the readout is where the joint is right now. Drag fast and the readout lags a moment while the motor catches up.

Loading the simulation. The robot runs in your browser, so the first one takes a few seconds to arrive.

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This is easier on a larger screen, but it works here too.

What you saw

The red tip of the first hinge drew a circle, and at the two ends of the slider it sat in the same place. Nothing stops that hinge, so it can turn all the way round. Its slider runs from −180° to +180° because a slider has to end somewhere, but those two ends are one pose, half a turn from the start either way. A slider is a straight thing standing in for a circle.

The green block did not turn at all. It went along its rail and back, and its readout gave centimeters where every other readout gave degrees. That is the whole difference between the two kinds of joint, in the one number that describes each.

The blue lever stopped at 90°, leaning on a peg, and the slider would not go further. Each of those two pegs marks a joint limit: the furthest the joint can go in that direction. On a real robot a limit is sometimes a real peg like that one, sometimes the next link getting in the way, and sometimes a cable that would tear. Whatever the reason, the robot's computer is told both ends and never commands the motor past them. In the box, every slider that ends short of a full turn ends at a joint limit of the model; only the first hinge has none. Your elbow has them too: it stops straight, and it stops folded.

The yellow ball turned three separate ways without leaving its socket. A ball joint lets a link turn every way about one fixed center. Your shoulder and your hip are ball joints. It takes three numbers to say where one is, so it counts for three degrees of freedom, which is why your shoulder counted for three in the last module. One honest note: the ball in this box is built from three hinges whose axes all pass through its center, one per slider. That is what a ball joint amounts to, and it is how robots build one: a motor's shaft turns about one line, which is exactly what a hinge does, and no motor turns a ball every way at once.

The purple pair showed the thing that turns joints into an arm. When you moved the first hinge, the second one and its link swung along, because they are bolted to the first link. When you moved the second, the first stayed put. Each joint moves everything after it in the chain and nothing before it. Add a third, a fourth, and a hand on the end, and you have the arm from the last module.

Why most robots are made of hinges

Look at almost any robot arm and you will find hinges all the way from base to hand, and no slides at all. The reason starts with the motor.

An electric motor turns. Its shaft spins, and that is the only thing it does. To make a hinge, you fix one link to the motor's body and the other to its shaft, and you are done: the motor's own turning is the joint's turning. To make a slide, you need something to turn that spinning into pushing, such as a long screw or a belt, plus a rail for the moving link to run along. The rail must be as long as the travel, stay straight, and stay clean. Grit stops a slide because the block has to run along all that open rail; a hinge's moving surfaces are a small ring tucked inside the joint, where grit does not reach.

A hinge also folds. An arm made of hinges can curl up small and reach out far, the way yours does; a slide is as long as its reach even when idle. When a machine has to reach around things, hinges win.

Slides have their place, and it is wherever dead-straight motion matters more than reach: a 3D printer's head, the cutting head of a machine tool, a forklift's lift, a robot that runs on rails across a warehouse ceiling. A robot arm gives up that straightness for a motor on every joint and a body that folds.

Next time you see a robot, look at each joint and ask which of the two it is: a hinge with a motor turning it, or a slide with something turning a motor's spin into a push. Then look for the limits. Every robot is a handful of doors and drawers, each one stopped at both ends.