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Introducing differential kinematics to mechanical engineering students

机译：向机械工程专业的学生介绍差速运动学

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摘要

Differential kinematics offers a simplified alternative to closed-form input-output equations needed to study the geometrical behaviour of linkages. For most linkages, these closed-form equations are either too messy or not possible to obtain, a fact that sometimes reflects negatively on how mechanical engineering students perceive the subject of mechanism analysis. On the other hand, differential models can easily be utilised in numerical methods designed to encourage these students to tackle even more difficult problems than currently being considered in academic programmes. In this paper, an approach is presented to facilitate this process. The mathematical procedure is based on the use of matrices referred to as kinematic Jacobians. The determinants of these matrices offer invaluable insights into the linkage mobility. These matrices are explained and used in a practice numerical example.
机译：微分运动学是研究连杆机构几何行为所需的闭合形式输入输出方程的简化替代形式。对于大多数链接而言，这些封闭形式的方程式太混乱或无法获取，这一事实有时会对机械工程专业的学生如何看待机理分析这一主题产生负面影响。另一方面，微分模型可以很容易地用在旨在鼓励这些学生解决比目前学术课程所考虑的难题更大的数值方法中。在本文中，提出了一种促进此过程的方法。数学过程基于使用称为运动雅可比矩阵的矩阵。这些矩阵的决定因素提供了对链接移动性的宝贵见解。这些矩阵将在实际数值示例中进行说明和使用。

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