In this paper, the inverse kinematics solutions for 16 industrial 6-Degrees-of-Freedom (DOF) robot manipulators with offset wrists are solved analytically and numerically based on the existence of the closed form equations. A new numerical algorithm is proposed for the inverse kinematics of the robot manipulators that cannot be solved in closed form. In order to Illustrate the performance of the New Inverse Kinematics Algorithm (NIKA), the simulation results attained from NIKA are compared with those obtained from well-known Newton-Raphson Algorithm (NRA). The inverse kinematics solutions of two robot manipulators with offset wrists are given as examples. In order to have a complete idea, the inverse kinematics solution techniques for 16 industrial robot manipulators are also summarized in a table. (C) 2013 Elsevier Inc. All rights reserved.