Complex workpieces (2), particularly aeronautical components made of solid stock presenting a bottom wall (3) and at least one stiffening rib (4) transverse to the bottom wall, are machined using a device (1) having a tool head (6) furnished with a transmission component (7) rotatable about a relative longitudinal axis s (X), and a tool (22), typically a milling cutter, connected to the transmission component (7) and capable of piercing the transverse rib (4). The longitudinal axis (Y) of the tool (22) extends obliquely to the axis (X) of the transmission component (7) so that the stiffening rib (4) can be pierced at a point close to the bottom wall (3) of the workpiece (2). The device also incorporates a feeler mechanism (24) associated with the tool head (6) and designed to engage the bottom wall (3) during the movement of the tool (22) toward the machining location, in such a way that the position of the tool head (6) can be actively controlled and the tool deployed at a selected distance from the bottom wall.
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