KINEMATIC ISOTROPY AND THE CONDITIONING INDEX OF SERIAL ROBOTIC MANIPULATORS

The conditioning index of a serial robotic manipulator is defined in this article in terms of the reciprocal of its minimum condition number The condition number of a manipulator is defined, in turn, as that of its Jacobian matrix. Moreover in defining the Jacobian condition number a quadratic norm of the Jacobian matrix is needed. However, this norm, or for that matter any other norm, brings about dimensional inhomogeneities. It is shown here that by properly defining the said norm based on a weighting positive definite matrix, the dimensional inhomogeneity is resolved Manipulators with a conditioning index of 100% are termed isotropic, a six-axis isotropic manipulator being introduced. This manipulator has all its angles between neighboring revolute axes at 90-degrees and all its distances between neighboring axes identical; moreover these distances are identical to the offsets of those axes. The kinematic conditioning of wrist-partitioned manipulators is given due attention, and illustrated with some examples of industrial robots of this type.