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.

当前用于开发机械手雅可比矩阵的方法基于传统的运动学描述，例如 Denavit 和 Hartenberg 参数。当处理更复杂的空间操纵器时，这些矩阵的符号方程变得繁琐且计算效率低下，例如在生物力学领域中看到的那些。本文基于广义运动学方程开发了一种改进的雅可比开发方法，该方程将矩阵的偏导数与莱布尼茨定律（乘积规则）结合起来。结果表明，在 MATLAB® M-Files 中使用时，可以导出一组符号矩阵函数，以提高计算效率，并且适用于任何空间操纵器。使用关节臂组件和手的肌肉骨骼模型作为示例。