This work is devoted to an impedance grasping strategy for a class of standard mechanical systems in the port-Hamiltonian framework. We embed a variable rest-length of the springs of the existing impedance grasping strategy in order to achieve a stable non-contact to contact transition, and a desired grasping force. We utilize the port-Hamiltonian structure of standard mechanical systems. First, we utilize a change of variables that transforms the port-Hamiltonian system into one with a constant mass-inertia matrix. We then achieve impedance grasping control via a \emph{virtual spring} with a variable rest-length. The force that is exerted by the virtual spring leads to a dissipation term in the impedance grasping controller, which is needed to obtain a smoother non-contact to contact transition. Simulations and experimental results are given in order to motivate our results.