kinematic chain

A kinematic chain is what you get when you string links together with joints — a whole connected run of stiff parts and the movable connections between them. One link, on its own, just sits there; chain several links together with joints and you have a mechanism that can reach, fold, and pose. A robot arm is a kinematic chain: base, then a joint, then a link, then another joint, then another link, and so on out to the hand. The chain is the robot's whole mechanical skeleton, built from the two basic ingredients — rigid links and the joints that let them move.

The order and type of the links and joints set everything the chain can do. Each joint adds a way to move, and each link carries that motion a fixed distance further out, so the chain as a whole decides where the far end can travel and how it can be oriented. Engineers describe an arm just by listing its joints in order, like RRP — revolute, revolute, prismatic — which tells you at a glance how it bends and slides.

Chains come in two shapes. An open chain is a single line of links with a free end, like an arm reaching out into the air — flexible and far-reaching, but a bit floppy. A closed chain loops back on itself so the links form a ring, like a triangle of struts — far stiffer and stronger, but with less freedom to move. Most familiar robot arms are open chains; many high-precision and heavy-lifting machines use closed ones.