In this article, the concept of linearity number (LN) is introduced to measure the ''linearity'' of the equations of motion of a serial manipulator. This number is computable in closed-form and is an average quantitative index of the degree of linearity of the robot over a specified region in the joint space. The definition is flexible, allowing the user to create custom-made definitions according to his or her specific needs. Using the concept of LN and the developed computer package CADLOR, one can design the kinematic and/or inertial parameters of the robot such that the robot is completely linear (or as linear as possible) and obtain the corresponding equations of motion in closed-form. Three manipulators are used to illustrate the linearization algorithm. The relation between LN and the performance of a linear controller is demonstrated by a case study in which the first 3 links of a PUMA 560 type robot is considered. (C) 1996 John Wiley & Sons, Inc.