Goehler Craig M, Murray Wendy M
Department of Mechanical Engineering, Valparaiso University, Valparaiso, IN USA.
Adv Eng Softw. 2012 May;47(1):160-163. doi: 10.1016/j.advengsoft.2012.01.002.
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.
当前用于推导机械手雅可比矩阵的方法是基于传统运动学描述，如丹纳维特（Denavit）和哈滕贝格（Hartenberg）参数。当处理更复杂的空间机械手时，例如生物力学领域中所见到的那些机械手，这些矩阵的符号方程会变得繁琐且计算效率低下。本文基于广义运动学方程开发了一种改进的雅可比推导方法，该方程结合了运用莱布尼茨法则（乘积法则）的矩阵偏导数。结果表明，可以推导出一组符号矩阵函数，当在MATLAB® M文件中使用时，它们能提高计算效率，并且适用于任何空间机械手。以一个关节臂组件和手部的肌肉骨骼模型为例进行说明。
