In this article, we present a new procedure for the derivation of the linearized kinematics and dynamics of a flexible industrial robotic manipulator. We introduce the Lie groups of dual rotation and dual homogeneous transformation matrices, which are the basis for the derivation of dual twists. In addition, dual screws and dual screw transformation matrices are introduced, which are used for the development of a general and systematic linearization procedure for both kinematics and dynamics. This leads to expressions that are linearized in all the states associated with the elastic motion. The dynamic modeling procedure is based on Kane’s method, where the partial velocities and partial angular velocities are given as dual screws arranged as columns of dual projection matrices. The elasticity of the links is modeled by the assumed mode method. The presented procedure is implemented numerically for a 4-degrees of freedom manipulator and the simulation results are given.

中文翻译：

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使用双螺杆的柔性机器人机械手的运动学和动力学

在本文中，我们提出了一种用于推导柔性工业机器人机械手的线性化运动学和动力学的新程序。我们介绍了对偶旋转矩阵和对偶齐次变换矩阵的李群，它们是导出对偶扭曲的基础。此外，还引入了双螺杆和双螺杆变换矩阵，用于开发运动学和动力学的通用和系统线性化程序。这导致在与弹性运动相关的所有状态中线性化的表达式。动态建模程序基于 Kane 方法，其中部分速度和部分角速度以双螺旋形式给出，双螺旋排列为双投影矩阵的列。链接的弹性由假定模式方法建模。