The external wrench is so defined:$$ W_{\kern-3px e} := \left[ \begin{array}{l} F_e \ M_e \end{array} \right]_{6 \times 1}
- $F_e$ : Sum of all external Forces - $M_e$ : Sum of all external Moments So if we have an external wrench we can define the system as **In Equilibrium** (or grasping equilibrium) if we apply to it a *Controlled Wrench* $W_{\kern-3px c}$ , such that:W_{\kern-3px c} = - W_{\kern-3px e}
- $W_{\kern-3px c}$ can be imposed by a human hand (IRL), a robotic hand (Industry) or a virtual hand (VR). - $W_{\kern-3px c}$ the controlled wrench (3 forces and 3 moments) represents the overall effect in term of forces and moments on the barycenter of the object, given by all the **contact forces** applied by the human/robotic/virtual hand at the contacts established with the object.