What a chain really is
A robot arm is not one solid piece. It is a row of stiff parts—called links—connected by movable hinges and sliders, called joints. Connect a few of these in sequence and you have a kinematic chain: a string of rigid bodies in which each joint lets the next part move relative to the one before it.
Your own arm is the cleanest example. Upper arm, forearm, and hand are the links; shoulder, elbow, and wrist are the joints. Each joint adds a way to move, and the parts beyond it ride along. Move your shoulder and the whole arm swings; bend just your wrist and only the hand turns. That is a chain at work: motion accumulates as you travel down it.
Joints come in several types, but two cover most robots. A revolute joint rotates, like a hinge or your elbow; a prismatic joint slides in a straight line, like a drawer or a telescoping pole. Whichever you use, the rule is the same: links carry the structure, joints carry the motion, and the order you chain them in decides what the whole thing can do.
Open chains and closed chains
Here is the fork in the road. Once you have a chain, ask one question: does it loop back on itself, or does it dangle free at the end? The answer splits every robot mechanism into two families—an open versus closed chain.
An open chain is a free arm with one loose end. Trace it from the base and you reach the tip without ever coming back—exactly like your arm reaching out from your shoulder to your fingertips. The far end, where the gripper or hand sits, is the end-effector: the part that actually touches the world. Nothing holds it in place but the chain behind it.
A closed chain loops back. Somewhere downstream the links rejoin, forming a ring instead of a free end. The classic example is the four-bar linkage: four links and four joints arranged in a closed loop, the shape behind everything from pliers to a car's suspension. Your own body does this too. Stand with both feet planted and you form a closed loop—floor, left leg, hips, right leg, back to the floor—which is exactly why standing on two feet feels so much steadier than holding one leg out in the air.
The trade: reach versus stiffness
Why does the loop matter so much? Because open and closed chains trade off the two things a mechanism cares about most: how far it can reach and how firmly it holds.
An open chain reaches far and moves freely. With a loose end, every joint can do its own thing, so the tip can swing through a large, generous workspace and twist into awkward poses—think of reaching behind a shelf. But that freedom has a cost: each joint stacks its small wobble on top of the last, and the whole arm flexes under load. Push on the tip and it gives, like a fishing rod bending.
A closed chain is stiff but constrained. Because the loop ties the moving part to the base through more than one path, the load is shared across several links instead of riding down a single arm. The result is rigidity and precision—it barely flexes under load—and for its size it can often carry far more weight. The price is freedom: the loop locks the parts together, so they can no longer move independently, and the region the end can reach shrinks.
So the choice is rarely "which is better"—it is "which problem are you solving?" Need to paint a whole car body or reach into a cluttered bin? Pick the open, far-reaching arm. Need to position a camera or a cutting tool with rock-steady precision? Pick the closed, stiff loop. The loop you draw is really a bet on reach versus stiffness.