System for positioning a surgical device

A surgical system comprising:

• a surgical device comprising:
• a base configured to be held in a user's hand,
• an end-effector for mounting a surgical tool or a tool guide for guiding the surgical tool, said surgical tool being configured to treat a planned volume of a part of a patient's body,
• a motorized actuation unit connected to said base and said end-effector for moving said surgical tool or tool guide with respect to the base in order to treat said planned volume;
• and
• a positioning system configured for positioning said surgical device relative to the part to be treated, the positioning system comprising:
• (i) a tracking unit configured to determine in real time the pose of at least one of the tool, the end-effector and the base with respect to the part to be treated,
• (ii) a control unit configured to:
• (a) compute in real time a working space of the surgical tool for said determined pose, wherein the working space is a union of all poses of the surgical tool relative to the base when a motor of the actuation unit is activated from a minimal value to a maximal value,
• (b) compute in real time the volume that remains to be treated to achieve the treatment of the planned volume, and
• (iii) a user interface coupled to the control unit and configured to display together:
• (a) the planned volume, said planned volume comprising a volume that remains to be treated and, if applicable, an already treated volume, and
• (b) the working space of the surgical tool.