Lab
6-axis robot arm
Six small motors, a gripper and a little trigonometry. Move the sliders and watch where the tip of the arm goes. Then try the reverse: which angles take the tip to a target?
Drag the scene to orbit around it. Measurements are in millimetres: x forward, y left, z up.
Lab
6-axis robot arm
What's going on?
Three ideas, one arm
- 01
What is a degree of freedom?
Each independent direction a joint can move in is called a degree of freedom (DOF). Each of the six servo motors in this arm turns around a single axis, so the arm has 6 degrees of freedom. Three are enough to reach a point in space: forward-back, left-right, up-down. The other three decide which way the tip faces once it gets there.
- 02
Forward kinematics: from angles to position
If you know every joint angle, you can work out where the tip is. Start at the base and add each segment’s length in the direction of the sum of the angles so far. With the shoulder at 90° the upper arm lies flat; if the elbow is at 0° too, the forearm continues in the same line. The x, y, z numbers in the lab come from exactly this calculation.
r = a₂·sin θ₂ + a₃·sin(θ₂+θ₃) + a₄·sin(θ₂+θ₃+θ₄) · x = r·cos θ₁, y = r·sin θ₁
- 03
Inverse kinematics: from position to angles
The reverse is harder. A target often has more than one set of angles (elbow up or elbow down), and sometimes none: the target is outside the arm’s reach. The lab’s inverse kinematics view solves it with a triangle. Try it yourself first, then compare with the angles it finds.
A tip for the tasks
Getting the arm within 10 mm of the target is enough. First turn the base towards the target, then reach with the shoulder and elbow, and set the wrist last. For the basket at the back, turning the base may not be enough: try tilting the shoulder backwards.
Try it yourself
Two short tries
This time there is no helper and the sliders move in 5-degree steps. When you press Check, the tip position is recalculated from your angles. You don’t need an account; nothing is saved here.
Robot arm · challenge
Grab the cube
Robot arm · challenge
Reach the box on the right
More simulations
Angles, forces and motion don’t stop here. In the journeys, other simulations are waiting for you, from pendulums to electric circuits.