my question is that I have a system of three links, all connected by spherical joints. There's three joints. I have the coordinates of all three joints labeled $a$, $b$ and $c$, plus the end-effector point called $d$. Now I need the rotation matrix for the last link.
I've been told by a friend that I can create 2 vectors, $v_1 = d-c$ (this is the first column of the orientation matrix) and $v_2 = b - c$. The cross product $v_3 = v_1\times v_2$ is the second column of the rotation matrix and $v_1\times v_3$ will give a vector that is perpendicular to both (the third column of the rotation matrix). Can someone please tell me if this is the correct method? Also, what is this method called? I have searched and searched but I cannot find this online. Thanks!