Disclosed is a surgical ancillary device, preferably Y-shaped, including three contact portions intended to come into contact with three corresponding reference areas of an operation area, and a unit for determining an orientation coordinate system of the ancillary device in a Galilean orientation coordinate system. At least one of the first and second contact portions, and preferably both, includes a concave or convex end, for example a roller that is optionally mounted so as to be rotatably movable, or a gutter-shaped element. Each end comes into contact with two reference points in the corresponding reference area, which is respectively convex or concave. These two points accurately guide the rotation of the ancillary device in order to bring the third contact portion into contact with the third reference area. The orientations of the ancillary device define the orientation coordinate system, the determination of which can therefore be accurately reproduced.
