Joints and degrees of freedom, made moveable
Every robot is a chain of joints, and every joint is defined by exactly one thing: how many independent motions it allows. Drive each joint yourself, move a rigid body through all six of its freedoms, and count mobility the way the exam asks you to.
The seven lower-pair joints
Pick a joint and watch it run. The bars on the right show the independent parameters that describe its motion — that count is the degree of freedom of the joint. Watch the screw and the cylindrical joint side by side: they look alike, but one has its rotation and translation locked together.
- Motion
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- Constraints
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- Found in
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Six degrees of freedom of a free rigid body
An unconstrained body in space needs six numbers to be fully described: three to say where it is, three to say which way it faces. Drag the sliders and watch the pose readout — this is the target that a manipulator has to be able to hit.
Position
Orientation
Serial arm playground — forward kinematics
Add or remove revolute joints and drive each one. Planar task space needs three numbers (x, y and tool angle φ), so watch what happens when the arm has fewer joints than that, exactly that many, or more.
Joints in the chain
End-effector pose
Mobility calculator — Grübler & Kutzbach
Count the links (include the fixed one), count the joints by type, and the criterion returns the mobility of the whole assembly. Load a preset to check your method against a mechanism you already know.
Configuration
Presets
Result
Check yourself
Eight questions in the style GATE asks them. Pick an answer to see the reasoning immediately.