Computational development of Jacobian matrices for complex spatial manipulators

Current methods for developing manipulator Jacobian matrices are based on traditional kinematic descriptions such as Denavit and Hartenberg parameters. The resulting symbolic equations for these matrices become cumbersome and computationally inefficient when dealing with more complex spatial manipulators, such as those seen in the field of biomechanics. This paper develops a modified method for Jacobian development based on generalized kinematic equations that incorporates partial derivatives of matrices with Leibniz’s Law (the product rule). It is shown that a set of symbolic matrix functions can be derived that improve computational efficiency when used in MATLAB® M-Files and are applicable to any spatial manipulator. An articulated arm subassembly and a musculoskeletal model of the hand are used as examples.

► Product rule can be applied to homogeneous transformation matrices to compute manipulator Jacobian matrices.
► Use of equivalent angle-axis rotation matrices allows application of proposed method to any manipulator.
► Proposed method is easily implemented within MATLAB®.