Manipulator kinematics is concerned with the motion of each link within a manipulator without considering mass or force. In this article, which is the first in a two-part tutorial, we provide an introduction to modelling manipulator kinematics using the elementary transform sequence (ETS). Then we formulate the first-order differential kinematics, which leads to the manipulator Jacobian, which is the basis for velocity control and inverse kinematics. We describe essential classical techniques which rely on the manipulator Jacobian before exhibiting some contemporary applications. Part II of this tutorial provides a formulation of second and higher-order differential kinematics, introduces the manipulator Hessian, and illustrates advanced techniques, some of which improve the performance of techniques demonstrated in Part I. We have provided Jupyter Notebooks to accompany each section within this tutorial. The Notebooks are written in Python code and use the Robotics Toolbox for Python, and the Swift Simulator to provide examples and implementations of algorithms. While not absolutely essential, for the most engaging and informative experience, we recommend working through the Jupyter Notebooks while reading this article. The Notebooks and setup instructions can be accessed at https://github.com/jhavl/dkt.

翻译：机械臂运动学关注的是机械臂各连杆的运动，而不考虑质量或力。作为两篇教程的第一篇，本文介绍了如何使用基本变换序列（ETS）对机械臂运动学进行建模。随后，我们推导了一阶微分运动学，进而得到机械臂雅可比矩阵，这是速度控制和逆运动学的基础。我们阐述了依赖机械臂雅可比矩阵的经典技术方法，并展示了部分当代应用。本教程第二部分将介绍二阶及高阶微分运动学的公式化表达，引入机械臂海森矩阵，并阐述先进技术，其中部分技术改进了第一部分所展示方法的性能。我们为教程的每节内容提供了Jupyter Notebooks，这些Notebooks采用Python代码编写，并利用Robotics Toolbox for Python以及Swift Simulator提供算法示例和实现。为获得最佳参与感和学习体验，我们建议在阅读本文时同步操作这些Jupyter Notebooks。Notebooks及安装说明可访问https://github.com/jhavl/dkt获取。