I am going through different texts (Spong Robot Modeling and Control, Murray Mathematical Introduction to Robotic Manipulations) and I am seeing different Jacobians developed for the same RRRP Manipulator (the SCARA).
My misunderstanding is similar as presented in this question . Overall, I am trying to develop the forward kinematics and Jacobian for the SCARA robot using exponentials of twists to test my knowledge but keep coming to different conclusions. I have found in Peter Corke's Robotics, Vision and Control this statement:
...compared to the Jacobian of Sect.8.1, these Jacobians give the velocity of the end effector as a velocity twist, not a spatial velocity as defined on page 65. To obtain the Jacobian as described in Sect.8.1, we must apply the transformation...
$J^0 = \begin{bmatrix} I_{3x3} & -[t_{E}^0]_x \\ 0_{3x3} & I_{3x3} \end{bmatrix} J^V_0$
I can get to Murrays:
But I am trying to get to Spong's Jacobian:
Any help/clarification would be greatly appreciated!