Robotic Arms: Joints, Axes & Inverse Kinematics
Move joints. Solve angles. Reach targets.
Move joints. Solve angles. Reach targets.
A robotic arm is a chain of rigid segments called links, connected by movable joints. The end of the chain is the end effector: a gripper, welder, paintbrush, or surgical tool.
Hover over each joint to learn what it does.
The word "robot" comes from the Czech word robota, meaning forced labor. It first appeared in a 1920 play by Karel Capek.
Each joint adds a degree of freedom (DOF) to the arm. More DOF means more flexibility, but also more complex math to control. Click each card to highlight that joint.
Rotates left/right (yaw)
Lifts up/down
Extends/folds
Rotates/tilts
Forward kinematics answers: "Given these joint angles, where does the end effector end up?" Adjust each joint angle below and watch the arm move.
Inverse kinematics is the reverse problem: "I want the end effector here. What joint angles do I need?" This is how real robots plan their movement. Click anywhere on the canvas to set a target.
Click anywhere to set a target for the arm.
Forward kinematics has one answer. Inverse kinematics can have zero, one, or many solutions. Your elbow can bend two ways to reach the same point. With more joints, the number of possible configurations explodes.
The kinematics you just explored powers arms in factories, hospitals, and even outer space.
Welding, painting, and assembling cars at superhuman speed and precision.
Da Vinci surgical robots use 7-DOF arms for minimally invasive procedures.
The ISS Canadarm2 is a 7-DOF arm that captures spacecraft and supports spacewalks.
Pick-and-place arms sort, package, and palletize products 24/7 without breaks.
There are over 3.9 million industrial robots operating worldwide as of 2024, with the automotive and electronics industries using the most.
You've explored how robotic arms calculate joint angles to reach any point in space. That math powers every factory robot, surgical tool, and space rover arm on Earth.
Robotic arms are chains of rigid links connected by joints that rotate or slide.
Each joint adds a degree of freedom. Most industrial arms have 6 DOF to reach any position and orientation.
Given all joint angles, calculate where the end effector ends up. Straightforward but limiting.
Given a target point, calculate what joint angles are needed. Harder to solve, but how real robots plan motion.
Put your new knowledge into practice!