Questions and Answers

Q: I have a question about the planar manipulator. In order to get the coordinates of Ptip, we do F1F2F3a3. Each F1, F2, F3 is relationship to the universal coordinate system or relative to each other? If it is to the
universal system, then how deltaF is defined? Also to the universal system?

A: Intuitively I thought F1 is relationship between the torso base and the universal coordinate system, then F2 is relationship between torso base to arm base, then F3 is arm base to forearm base, then the hand as the tip.


Q:

A: Reasonable question.  As I described it in class I was describing Fi in
terms of universal coordinates.  But in fact, the kinematic chain
is a sequence of coordinate transformations, each relative to the previous
one.

Thus, if F12 is the transformation from F1 to F2, we get

        F2 = F1 * F12

etc.  In this case, the position of the end effector is something like

        ptip = F3*a3

                = F2 * F23 * a3
                = F1 * F12 * F23 * a3
                = F0 * F01 * F12 * F23 * a3

        where F01 = [Rot(x,theta1),0]
              F12 = [Rot(x,theta2),a1]