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We introduce the notion of the Lie derivative in the context of dualquaternions that represent rigid motions and twists. First we define the wrenchin terms of dual quaternions. Then we show how the Lie derivative helpsunderstand how actuators affect an end effector in parallel robots, and make itexplicit in the two cases case of Stewart Platforms, and cable-driven parallelrobots. We also show how to use Lie derivatives with the Newton-Raphson Methodto solve the forward kinematic problem for over constrained parallel actuators.Finally, we derive the equations of motion of the end effector in dualquaternion form, which include the effect of inertia from the actuators.

Using Lie derivatives with dual quaternions for parallel robots