Abstract: The Jacobian matrix of a robot with both rotational and translational DOFs consists of entries have different units, which result in the difficulty to compute the dexterity measures of the robot. To solve this problem, a simple but effective method based on variable weighting matrix to normalize the Jacobian matrix is presented. The principles and disvantages of the traditional normalizing methods are analyzed, and based on the essence of robot dexterity, it is pointed out that the core problem of normalizing the Jacobian matrix is to properly relativize the two kinds of vectors of it, which correspond to the two kinds of velocities of the robot respectively. According to the definition of the Jacobian matrix condition number and the requirements of the isotropy, general ideas and methods for normalizing the Jacobian matrix are put forward, and the variable weighting matrix is defined. The variable weighting matrix is deduced just from the Jacobian matrix, and is used in turn to normalize the Jacobian matrix, therefore the disvantages of introducing additional parameters of the traditional methods are avoided. It proves that dexterity is an intrinsic property of the robot, and is independent of any parameters introduced. The validity of the variable weighting matrix is illustrated by the theoretical application to the 6R robot, and the numerical simulations on two typical robot manipulators.

Key words: dexterity, Jacobian matrix normalization, robot manipulator, variable weighting matrix