A kinematic structure-based classification of six degree-of-freedom industrial robotic manipulators is introduced, and a complete set of compact kinematic equations is given according to this classification. For the classification, 100 industrial robots are surveyed. These robots are first classified into main groups and then into subgroups under each main group, and nine kinematic main groups, each having 1-10 subgroups are obtained. The main groups are based on the end-effector rotation matrices and characterized by the twist angles. On the other hand, the subgroups are based on the wrist point positions and characterized by the link lengths and offsets. Compact kinematic equations are derived for all main groups and subgroups by utilizing the properties of exponential rotation matrices, and simplification tools derived by using these properties. Most of these simplified compact equations can be solved analytically and the remaining few of them can be solved semi-analytically through a single univariate equation. In these solutions, the singularities and the multiple configurations of the manipulators can be determined easily. Using these solutions, the inverse kinematics can also be computerized by means of short and fast algorithms. (C) 2001 Elsevier Science Ltd. All rights reserved.