Assembly for machining a surface, characterized in that it comprises: - an effector comprising: • an electric spindle comprising a body having, at one of its ends, means for coupling to a cutting tool (O), • a first holder connected to the body of the electric spindle by a sliding connection allowing the electric spindle to move in translation along the axis Z of rotation of the tool, • a second holder connected to the first holder by a sliding connection allowing the first holder to move in translation along an axis X perpendicular to the axis Z of rotation of the tool, • a frame , one of the ends of which constitutes a foot and the other of the ends of which constitutes a head designed to be coupled to the free end of a robot arm, the frame being connected to the second holder by a sliding connection allowing the second support to move in translation along an axis Y perpendicular both to the axis X of translation of the first holder and to the axis Z of translation of the electric spindle and of rotation of the tool; - at least one bearing element (10; 93) for the foot of the effector, intended to be arranged on the surface to be machined or on tooling that supports the surface, the bearing element and the foot of the effector being configured such that the effector is connected to the surface to be machined or to the tooling that supports the surface by a ball joint connection when the foot of the effector is in contact. - an effector comprising: • an electric spindle comprising a body having, at one of its ends, means for coupling to a cutting tool (O), • a first holder connected to the body of the electric spindle by a sliding connection allowing the electric spindle to move in translation along the axis Z of rotation of the tool, • a second holder connected to the first holder by a sliding connection allowing the first holder to move in translation along an axis X perpendicular to the axis Z of rotation of the tool, • a frame , one of the ends of which constitutes a foot and the other of the ends of which constitutes a head designed to be coupled to the free end of a robot arm, the frame being connected to the second holder by a sliding connection allowing the second support to move in translation along an axis Y perpendicular both to the axis X of translation of the first holder and to the axis Z of translation of the electric spindle and of rotation of the tool; • an electric spindle comprising a body having, at one of its ends, means for coupling to a cutting tool (O), • a first holder connected to the body of the electric spindle by a sliding connection allowing the electric spindle to move in translation along the axis Z of rotation of the tool, • a second holder connected to the first holder by a sliding connection allowing the first holder to move in translation along an axis X perpendicular to the axis Z of rotation of the tool, • a frame , one of the ends of which constitutes a foot and the other of the ends of which constitutes a head designed to be coupled to the free end of a robot arm, the frame being connected to the second holder by a sliding connection allowing the second support to move in translation along an axis Y perpendicular both to the axis X of translation of the first holder and to the axis Z of translation of the electric spindle and of rotation of the tool; - at least one bearing element (10; 93) for the foot of the effector, intended to be arranged on the surface to be machined or on tooling that supports the surface, the bearing element and the foot of the effector being configured such that the effector is connected to the surface to be machined or to the tooling that supports the surface by a ball joint connection when the foot of the effector is in contact. <EOS>