# The Jacobian resulted from Screw method is different from analytical one (Example Inside)

I am currently solving a kinematics example that asks for the Jacobian. However, when I solve it using the Screw method I get different results from the analytical method, The example is kinda hard to write here but I will demonstrate on a 2D RR robot which shows the same behavior.

Here is the simple problem: Now lets find the Jacobian when $$θ_1=pi/4$$ while $$θ_2=0$$, $$L1=L2=1$$

Here is the Jacobian using Screw Method:

$$J = \begin{bmatrix} 0 & 0\\ 0 & 0 \\ 1&1 \\ 0& 0.7\\ 0& -0.7\\ 0&0 \end{bmatrix}$$

Here is the Jacobian using Analytical Method:

$$J = \begin{bmatrix} -L_1 sin(θ_1) - L_2 sin(θ_1+θ_2) & -L_2 sin(θ_1+θ_2)\\ L_1 cos(θ_1) + L_2 cos(θ_1+θ_2) & L_2 cos(θ_1+θ_2) \\ \end{bmatrix},$$

$$J = \begin{bmatrix} -\sqrt{{2}} & -\sqrt{{2}} / 2 \\ \sqrt{{2}} & \sqrt{{2}} / 2 \\ \end{bmatrix}$$

Notice that even singularity of both methods do not match. Where did I make the mistake?

Also, why the screw method does not take into account the length of last link? I mean if the length of last link is 0 or 1000, the linear velocity W x R should change.

Edit1: Here is the method I used to calculate the first jacobian. • Can you provide sources of formulae you were using? It seems to me that they are Jacobian of different equations. The first one maybe maps joint velocities to a screw. The second one maps joint velocities to tool velocities. – Petch Puttichai Nov 18 '19 at 13:26
• @PetchPuttichai I have updated the question with the method used to calculate the first jacobian. The second one is simply FwD kinematics then differentiation. – Forenkazan1 Nov 18 '19 at 18:31
• I haven't had time to get back to this yet. But I guess both of them are representing the same thing. Maybe if you try writing the 6D tool twist (from the equation with screw method Jacobian) in terms of just $\dot{x}$ and $\dot{y}$, you might get the tool x-y velocity similar to what you'd get from using the equation with analytical method. – Petch Puttichai Nov 25 '19 at 11:34
• The first one, based on screw theory does not seem right. Could you complete the question with an indication how was it derived? – 50k4 Jun 4 at 19:02