论文标题
使用双重四合一的谎言衍生物作为平行机器人
Using Lie derivatives with dual quaternions for parallel robots
论文作者
论文摘要
我们在代表僵化动作和曲折的双重四季度的背景下介绍了谎言衍生物的概念。首先，我们根据双重四元素来定义扳手。然后，我们展示了谎言衍生物如何帮助了解执行器如何在平行机器人中影响最终效应器，并在两种情况下，在Stewart平台的两种情况下显式，以及电缆驱动的并行机器人。我们还展示了如何使用牛顿 - 拉夫森方法使用谎言衍生物来解决过度约束的平行执行器的正向运动问题。最后，我们以双重四基因形式得出了末端效应器的运动方程，其中包括执行器的惯性作用。
We introduce the notion of the Lie derivative in the context of dual quaternions that represent rigid motions and twists. First we define the wrench in terms of dual quaternions. Then we show how the Lie derivative helps understand how actuators affect an end effector in parallel robots, and make it explicit in the two cases case of Stewart Platforms, and cable-driven parallel robots. We also show how to use Lie derivatives with the Newton-Raphson Method to solve the forward kinematic problem for over constrained parallel actuators. Finally, we derive the equations of motion of the end effector in dual quaternion form, which include the effect of inertia from the actuators.
