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Herein is proposed a concise algorithmic procedure for deriving a minimum l∞-norm solution of the system of consistent linear equations Ax=b, where A is a m×n matrix, b is given as a m×1 vector and x is a n×1 unknown vector. The proposed algorithm is developed based on the geometrical analysis of the characteristics of the minimum infinity-norm solution. The proposed algorithm is well-structured so that it may be implemented easily through simple linear algebraic manipulation. For the case of nm, the basic idea of the method is extended to finding internally mapped vertices when a n dimensional polytope is transformed into m dimensional polytope through consistent linear mapping A. The proposed method is applied to the task velocity analysis for robot manipulators with joint velocity constraints.