The analogy between Equations (3.20) and (4.5) by means of the Jacobian makes it interesting to analyze Equation (4.5) similarly to what we did in Sections 3.3 and 3.4.3. This analogy is defined as kineto-statics duality, and helps the novice roboticist to more intuitively correlate these two levels of abstraction.
In a singularity both the Jacobian and its transpose lose rank. That means that in a singularity a robot moves very fast and very hard and strikes anything in its way with a lot of force. Ouch!