With direct kinematics for an ordinary manipulator, everything is pretty simple. And what about the inverse? At a minimum, it’s worth to repeat that it is ambiguous. Let’s start with the two-links manipulator.
From the direct we know:
We squared both and add. Find :
find as: . Bottom sign if shoulder down in 4th quarter or
Now is easy to find , and
Not so beautiful. And what for 3-links ?
Let’s start with a familiar manipulator. Obvivious, . And the rest is above discussed 2-links manipulator.
It means we moved the origin to and rotated the axes to along .
Great, but what if we have a planar 3-links manipulator?
Then we can not cope without additional knowledge, namely, without knowledge of orientation the tip . The rotation will only be around z, so remembering what is H you can understand, that .
And then by default:
As you understand, it was all told in order to be the basis for calculating the kinematics of 6-links manipulator day in the next article.