Degrees of freedom
This page shows how a point moving in a cube can be used to represent the possible positions of a robot with three two-dimensional joints (that is, which allow a constrained movement on a plane).
The robot must travel from the initial position (represented by the blue box) to the final position (the yellow box), without colliding with the obstacle (represented by the red box).
On the right you see a 3D graph where each point inside the cube represents a possible state of the robot. Click & drag on the graph allows you to change the point of view. The three cursors at the bottom left allow you to move the robot. The arrows change display modes:
- You can move the robot as you like.
- The red volumes in the graph show the locations where a part of the robot collides with an obstacle (the red box).
- A path is highlighted that allows the robot to touch the yellow square and them move to touch the blue square, without colliding with the obstacle.
4. The robot moves along the path.
Please note: why is this animation in the 4D category if we are talking about a 3D cube and a 2D mechanical arm?
It’s easy to imagine: a moving point in a 4D hypercube represents the possible positions of a similar robot with 4 joints.
A robot that has only two joints, not constrained to a plane, but moving in space can require 4 dimensions or even more depending on the possible degrees of freedom of the movement for each joint.
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