Sensing, Actuating and Controlling
Kinematics & Degrees of Freedom
14 min · 2 worked examplesFree
Describing where a machine can go, converting joint angles into positions, and the harder problem of going the other way.
After this lesson you can
- Count the degrees of freedom a task needs
- Work forward kinematics from joint angles
- Say why inverse kinematics can have several answers or none
Degrees of freedom
A degree of freedom is one independent way something can move. A free body in space has six: three translations and three rotations.
A robot has as many degrees of freedom as it has independent joints. To place a gripper anywhere in a plane at any angle needs three; to do the same in space needs six.
Fewer than the task requires means positions that simply cannot be reached, whatever the control system does. More than required is redundancy, several joint combinations reach the same point, which allows a machine to work around an obstacle and makes the mathematics harder because there is no longer a single answer.
Counting degrees of freedom against the task is the first check on any mechanism, and it is done on paper long before anything is built.
In the full lesson
- Degrees of freedom
- Forward kinematics
- Inverse kinematics
Free with an account. Read it, work the examples, answer the questions, then build it in the simulator.