A semi-analytical method and an associated computer program are developed for inverse kinematics solution of a class of robotic manipulators, in which four joint variables are contained in the wrist point equations. For this case, it becomes possible to express all the other joint variables in terms of a selected one. and this reduces the inverse kinematics problem to solving a non-linear scalar equation having the selected joint variable as the only unknown. The solution can be obtained by iterative methods and the remaining joint variables can easily be computed by using the solved joint variable. Since the method is manipulator dependent, the equations will be different for kinematically different classes of manipulators, and should be obtained analytically in a similar way as done here, using the suggested algebra based on exponential rotation matrices. A significant benefit of the method is that the singular configurations and multiple solutions indicated by sign ambiguities can be determined while deriving the inverse kinematic expressions. The developed method is applied to a six-revolute-joint industrial robot, FANUC Arc Mate Sr. (C) 2000 Elsevier Science Ltd. All rights reserved.