# Dexterity calculation with dual quaternions

How can the manipulability of a robot arm be calculated when the kinematics are described with screw theory such as dual quaternions? These methods are sigularity-free, but what could we say about dexterity?

$$\mathit{w}(q) = \sqrt{det(\mathbf{J}(q)\mathbf{J}^T(q)}$$