The Inverse Kinematics (IK) problem consists of finding robot control parameters to bring it into the desired position under the kinematics and collision constraints. We present a global solution to the optimal IK problem for a general serial manipulator with 7 degrees of freedom (7DOF) with revolute joints and a quadratic polynomial objective function. We show that the kinematic constraints due to rotations can all be generated by second degree polynomials. This is important since it significantly simplifies the application of the Lasserre relaxations on the non-convex polynomial system. We demonstrate that the second relaxation is sufficient to solve the 7DOF IK problem on a KUKA LBR IIWA manipulator and we show that we are able to compute the optimal IK or certify infeasibility in 99% of the tested poses. This is joint work with Pavel Trutman (Prague), Tomas Pajdla (Prague) and Mohab Safey El Din (Paris).