# Problem with solution (equation) for wrist singularity

In my textbook about industrial robots it says that if the angle q5 in this robot is equal to 0, there are infinite solutions for the angles q4 and q6. I understand this part, but I have a problem with the equation below.

As a solution for this the book says f(q4,q6) = c1*(q4A - q4)^2 + c2*(q6A-q6)^2 = MIN

q4A and q6A are the joint angles calculated from the previous backward transformation when driving a robot path.

By the above equation, a solution for q4 and q6 is taken which is closest to the previous solution.

Between two IK solutions (intermediate points) on a line that the TCP must travel, Q4 must rotate from -pi/2 to -3/2*pi, and Q6 must rotate from pi/2 to -pi/2. Both joints must therefore cover a rotation of -pi.

So the formula would be: c1*(-pi/2 - (-3/2*pi))^2 + c2*(pi/2-(-pi/2))^2

Since I do not know c1 and c2 and the book does not tell me how to determine them, I cannot calculate a solution. How do I calculate the angles for Q4 and Q6?

• Hi, Can you provide the name of the book, author and page? There is missing information to your question and is hard to answer. Feb 17 '20 at 14:00
• Industrieroboter: Methoden der Steuerung und Regelung from Wolfgang Weber. Page 47 equation 3.3, its german... Feb 17 '20 at 14:03
• I tried to find the book to see the full equations but I couldn't. Unfortunately I cannot provide an answer since I am lacking the full context. I believe these c1 and c2 comes as constant terms in the previous equations in the book. Feb 24 '20 at 11:03