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Structure Based Classification and Kinematic Analysis of Six-Joint Industrial Robotic Manipulators

In this chapter, a complete set of compact, structure based generalized kinematic equations for six-joint industrial robotic manipulators are presented together with their sample solutions. Industrial robots are classified according to their kinematic structures, and their forward kinematic equations are derived according to this classification. The purpose of this classification is to obtain simplified forward kinematic equations considering the specific features of the classified manipulators and thus facilitate their inverse kinematic solutions. For the classification, one hundred industrial robots are surveyed. The robots are first classified into kinematic main groups and then into subgroups under each main group. 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. The reason for preferring the wrist point rather than the tip point in this classification is that, the wrist point and rotation matrix combination contain the same amount of information as the tip point and rotation matrix combination about the kinematic features of a manipulator, and the wrist point coordinates are simpler to express in terms of the joint variables. After obtaining the forward kinematic equations (i.e. the main group rotation matrix equations and the subgroup wrist point equations), they are simplified in order to obtain compact kinematic equations using the numerous properties of the exponential rotation matrices (Ozgoren, 1987-2002). The usage of the exponential rotation matrices provided important advantages so that simplifications are carried out in a systematic manner with a small number of symbolic matrix manipulations. Subsequently, an inverse kinematic solution approach applicable to the six-joint industrial robotic manipulators is introduced. The approach is based on the kinematic classification of the industrial robotic manipulators as explained above. In the inverse kinematic solutions of the surveyed industrial robots, most of the simplified compact equations can be solved analytically and the remaining few of them can be solved semi-analytically through a numerical solution of a single univariate equation. The semi-analytical method