Degrees of freedom & mobility¶
A rigid body floating free in space has 6 degrees of freedom (DOF): it can
translate along X, Y and Z, and rotate about each of those three axes.
Nothing constrains it, so all 6 are free — the only thing that decides how it
moves is whatever forces act on it. A body under gravity alone, with no
joints, just falls: textbook free fall, s = ½gt².
Every joint, spring or drive you add either removes some of those 6 DOF (a joint pins the body down to fewer possible motions) or loads the ones that remain (a force or torque pushes along a DOF without removing it). This is the one idea that runs through the whole tool: start from 6, and ask what's still free.
Counting DOF this way — 6 per body, minus what each joint removes, across a whole mechanism — is how engineers check a linkage can move, and how many independent motions it has, before ever running a solve. It's known as a Grübler / mobility count.