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The inverse kinematics problem of robot manipulators is solved analytically in order to have complete and simple solutions to the problem. This approach is also called as a closed form solution of robot inverse kinematics problem. In this paper, the inverse kinematics of sixteen industrial robot manipulators classified by Huang and Milenkovic were solved in closed form. Each robot manipulator has an Euler wrist whose three axes intersect at a common point. Basically, five trigonometric equations were used to solve the inverse kinematics problems. Robot manipulators can be mainly divided into four different group based on the joint structure. In this work, the inverse kinematics solutions of SN (cylindrical robot with dome), CS (cylindrical robot), NR (articulated robot) and CC (selectively compliant assembly robot arm-SCARA, Type 2) robot manipulator belonging to each group mentioned above are given as an example. The number of the inverse kinematics solutions for the other robot manipulator was also summarized in a table.