Abstract: The present paper is stemmed from the common characteristics of the regional structures (the first three links) of various industrial robots. Taking a suitable base point coinciding with one of the origins of coordinate systems associated with the regional structure for calculating the linear velocity of the end-effecter, and selecting two appropriate coordinate systems out of those for projecting the linear velocity and angular velocity of the end-effecter, a kind of unified Jacobian matrices can be formulated and transformed into the triangular block type only through simple rearranging of rows. This type of triangular block matrices is called unified and simplified Jacobian matrix. As one of its diagonal sub-matrices is a constant sub-matrix, thus with the use of the simplified Jacobian matrix, the 6×6 Jacobian matrix can be treated as a 3×3 matrix, and the relevant kinematic analysis of industrial robots can be simplified. At the end of the paper one illustrating examples are given.

Key words: 机器人, 矩阵, 运动学