← Robot list · Learn the basics · Compare: industrial 6-axis robot
Move a slider, or click in a number box and type a value with your keyboard. With q = 0 for all joints, the arm is stretched out horizontally, towards −x (this is the real UR zero position). Like the real robot, every joint can turn ±360°.
Each joint is drawn with its symbol: a circle when its axis points towards you or away from you, and a thick bar along its axis otherwise. The orange line goes from the base to the tool. Axes: x red, y green, z blue. ⊙ points at you, ⊗ points away. The dashed squares are the pads A and B, and the blue square is the cube.
Frame i is attached to the axis of joint i+1.
Each row is: Ai = Rz(θ) · Tz(d) · Tx(a) · Rx(α).
Orange numbers are the current values. These are the real numbers Universal Robots publishes for the UR5:
the negative a values mean the arm folds back along −x, and there is no offset on any θ.
Frame i is attached to the axis of joint i.
Each row is: Ai = Rx(αi−1) · Tx(ai−1) · Rz(θ) · Tz(d).
The last column is the position of the tool flange (the plate where the gripper is bolted on) in the base frame {0}. The fingertips are another 0.10 m further along z6. The 3×3 block says where the tool points: its third column is the direction of z6. Both tables give exactly this same matrix.
Compare it with the industrial 6-axis robot. Here rows 4 and 5 have d4 and d5 ≠ 0: the three wrist axes do not meet at one point. This is the typical "offset wrist" of Universal Robots. The wrist is compact and cheap to build (three identical small joints), but the inverse kinematics cannot split into "position by joints 1-3, orientation by joints 4-6" as simply as for a spherical wrist. Still, the UR5 has a closed-form solution with up to 8 configurations (shoulder left or right × elbow up or down × wrist flipped or not); the page uses the numerical method to stay general.
A real cobot controller slows down or stops near these configurations.
| Industrial robot (FANUC, KUKA…) | Cobot (UR, FANUC CRX, ABB GoFa…) | |
|---|---|---|
| Fence / cage | Yes, almost always | Often none, if the risk assessment allows it |
| Payload | 5 to more than 1000 kg | about 3 to 25 kg |
| Speed | Very high | Limited, depending on the risk assessment |
| Sensing of contact | Fence, light curtains | Torque sensors or motor current in the joints |
| Programming | Teach pendant, code, a specialist | Hand-guiding (you move the arm by hand) and drag-and-drop screens |
| Moving it to a new job | Heavy job | Light enough to move on a trolley |
| Shape | Powerful, sharp edges possible | Rounded, no pinch points, light |
The standards ISO 10218 and ISO/TS 15066 describe four ways of working next to a person:
Important: a cobot is safe only with its tool and its task. A sharp tool or a heavy fast load can make the whole cell dangerous again, so the risk assessment is done for the complete application, not for the arm alone.
The demo says "put the tool at this point, pointing down" and the page finds the 6 joint angles. The solver starts from a typical UR "ready" pose (0, −90, 90, −90, −90, 0) and uses a numerical method:
1. compute where the tool is now (forward kinematics) 2. compute the error between the target and the tool 3. use the Jacobian to find the small joint changes that reduce the error 4. repeat until the error is below 0.01 mm
The tool must point straight down, with the fingers along x. The numbers below are for the fingertips; the solver aims the flange 0.10 m higher. These are the angles it found (one of the 8 possible configurations):
Small and medium factories with many different small batches: machine tending, screwdriving and assembly, pick and place, packing and palletizing light boxes, quality inspection with a camera, gluing, dispensing, polishing, laboratories (pipetting, sample handling), food and cosmetics, and even coffee shops. Payloads go from 3 to about 25 kg, with a repeatability around ±0.03 mm. Well-known makers: Universal Robots (UR3e to UR20), FANUC CRX, ABB GoFa and SWIFTI, KUKA LBR iisy, Doosan, Techman, Franka Emika (7 axes), Kinova.
Yes, a pinch gripper (pince) works, like the two-finger one in the 3D model; electric grippers such as the Robotiq 2F-85 are the most common choice. Because a cobot works near people, tools are chosen to be safe too: rounded fingers, limited gripping force. Other tools: