Links, joints, motors, and the bit of geometry that turns "put the hand there" into joint angles. Read in order. Every figure with a slider or a handle can be operated.
An arm is a chain. The rigid pieces are links; what connects them are joints. The chain starts at a fixed base and ends at the end effector, the hand or tool that does the work.
Nearly every joint is one of two kinds. A revolute joint turns, like an elbow. A prismatic joint slides, like a drawer. Each lets the next link move in exactly one way.
Each independent joint adds one degree of freedom (DOF). Count them and you know how many ways the arm can move.
Why do so many factory arms have six? A rigid object floating in space has six things you can set: where it is (left–right, forward–back, up–down) and which way it faces (roll, pitch, yaw). To put a tool anywhere in its reach and point it any way, an arm needs at least six joints. Fewer, and some poses are impossible. More (seven is common on collaborative arms) and the arm has spare motion, so it can reach the same pose while swinging its elbow around an obstacle.
The figures that follow flatten the arm onto a page: two or three revolute joints in a plane. Every idea carries up to six joints in three dimensions; only the arithmetic gets longer.
Kinematics is the geometry of motion, ignoring the forces behind it. The easy direction is forward: given every joint angle, where does the hand end up? Add up the links, each turned by the angles before it.
The useful direction is backwards. A task says "pick up the part there"; the controller has to work out which joint angles get the hand to that spot. That is inverse kinematics (IK), and it is where arms get interesting:
For two links, IK has a tidy closed form. The law of cosines gives the elbow: cos θ2 = (x² + y² − L1² − L2²) / (2·L1·L2). Taking the positive or negative angle picks elbow-down or elbow-up. If that cosine comes out above 1 or below −1, the point is out of reach. Six-axis arms built with three wrist axes meeting at one point split the same way into a "where" problem and a "which way" problem, each with a closed form; arms without that layout are usually solved numerically, nudging the angles until the hand lands.
At certain poses the arm loses a direction it can move in. Stretch a two-link arm straight out: the hand can swing sideways but cannot move further out, however the joints turn. That pose is a singularity.
The other classic one: fold the arm back so the hand sits right over the shoulder joint. Now the shoulder angle no longer matters, since turning it just spins the hand in place, so the arm has lost a direction again.
The trouble shows up near them. Ask the hand to move in a straight line at a steady speed past a singularity, and the joints must spin faster and faster to keep up. Real controllers slow down, stop, or plan around them.
Every joint has the same small kit: something to turn it, something to multiply the force, something to measure where it is, and a controller closing the loop between them, thousands of times a second.
| Part | Common choices | What it trades |
|---|---|---|
| Motor | Brushless servo motor; stepper motor; hobby servo | Brushless servos are smooth and strong but need a proper drive. Steppers are cheap and hold position without sensors until overloaded, then silently lose steps. Hobby servos bundle motor, gears, and sensor for small arms. |
| Reducer (gearing) | Strain wave ("harmonic") gear; cycloidal drive; planetary gearbox; belts | Motors spin fast and weak; joints need slow and strong. Strain wave gears give high ratios with almost no backlash in a compact package, which is why wrists use them. Cycloidal drives take shock loads in big joints. Planetary gears are cheaper but have more play. |
| Sensor | Optical or magnetic encoder, incremental or absolute | An incremental encoder counts ticks from a known home; an absolute one knows its angle at power-on, so the arm needs no homing routine. |
| Brake | Spring-applied brake on each heavy axis | Holds the arm when power is cut, so it does not fold under its own weight. |
| Controller | Per-joint drive plus a motion controller | Turns a planned path into joint commands, checks limits, and compares where each joint is with where it should be. |
Reach: how far from the base the wrist can get. Payload: the mass it can carry at full reach, tool included. Repeatability: how closely it returns to the same taught point, often a few hundredths of a millimetre on industrial arms. Accuracy is different: how close it gets to a point given as coordinates, which depends on how well its link lengths and offsets are known. Most arms are far more repeatable than accurate.
The arm only moves the tool. The tool decides the job, and on many cells a tool changer swaps it automatically.
| Tool | Good for |
|---|---|
| Parallel-jaw gripper | Boxes, parts with flat faces; the default |
| Vacuum (suction) cups | Flat or smooth items: sheets, cartons, glass |
| Soft or finger grippers | Food and irregular, fragile shapes |
| Magnetic gripper | Steel parts |
| Process tools | Welding torches, spray guns, screwdrivers, dispensers, cameras |
Many tools add a force-torque sensor at the wrist, so the arm can feel contact: pressing a part home, sanding with steady pressure, or stopping when it bumps something.
Same parts, different layouts, each shaped by the job.
Revolute joints all the way, usually six. Reaches around things; the general-purpose shape for welding, painting, handling.
Two horizontal revolute joints plus a vertical slide. Stiff up and down, flexible side to side: fast, precise assembly on a flat table. The name means Selective Compliance Assembly Robot Arm.
Three light arms from an overhead base meet at one small platform. Very fast pick-and-place, small payloads; the classic packaging-line robot.
Three prismatic joints at right angles: x, y, z. Simple maths, easy to scale up, the same layout as most 3D printers and CNC routers.
Usually articulated, built to work beside people: rounded, lighter, and limited in force and speed so a bump stops it. Often taught by hand-guiding the arm through a move.