I am working on an forward kinematics geometric solution. What it roughly means is that given a certain $(x,y,z)$ co ordinates the robot should compute the angles at which it should move its arms.
I have a robot which looks like this,
While checking for geometric solution for the robot I came across this research paper where everything is explained almost,
but you can see that there is this factor $L4$ which has to be found in order to find the complete solution but I do not know how to find this $L4$ as this varies depending on the position, but in the research paper they have taken it as if its a constant. Is there a way on how I can find this $L4$ or is it really a constant? I will post the link to the actual research paper in the comments.
If I follow the diagrams right, then in Figure 3, $L_4$ is the $x$-coordinate of the point $p_2$. The $x$-coordinate of $p_1$ is $L_1\cos \theta_2$, while the difference in $x$-coordinates between $p_1$ and $p_2$ is $L_2\sin \theta_3$. So the answer should be $$L_4 = L_1\cos \theta_2 + L_2\sin \theta_3$$