# Developing world-frame Jacobian using product of exponentials [closed]

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!

• Welcome to Robotics NLhere, but I'm afraid that it is not clear what you are asking. We prefer practical, answerable questions based on actual problems that you face, so it's a good idea to include details of what you want to achieve, what you tried, what you saw & what you expected to see. Please take a look at How to Ask & tour for more information on how stack exchange works and work through the Robotics question checklist to edit your question to make it clearer. – Mark Booth Feb 26 '18 at 16:11
• What is the set of frames you are using and how does that compare with spongs frames? At a glance it appears that you are attaching your frames to the scara structure differently. Keep in mind that the math is independent of the physical structure and you can get many different jacobians based on how you choose to attach your frames. – hauptmech Feb 26 '18 at 21:00
• Thanks for the edit NLhere, but it's still unclear what you are asking. If you can include details of what you tried and what you saw it might help, as would the information requested by @hauptmech. – Mark Booth Feb 27 '18 at 14:21