A machine (100) for treating a surface (200) comprises a frame (110) having a rear portion (111) arranged to get in contact with the surface (200) at a contact line λ, a front portion (112) arranged to support an element of treatment (115), and a support element (130) arranged to pass between a retracted configuration, where the element of treatment (115) touches the surface (200), and an extended configuration, where the element of treatment (115) does not touch the surface (200). The frame (110) also comprises a reference plane n that is substantially coincident with the surface (200), when the support element (130) is in the retracted configuration, and arranged to rotate about the contact line λ forming an angle a with the surface (200), when the support element (130) passes in the extended configuration. The frame (110) also comprises a reference axis y at an angle a/2 with respect to normal z of the reference plane n. The support element (130) comprises a pivoting wheel (135) arranged to rotate about a rotation axis x. The support element (130) passes between the retracted configuration and the extended configuration by means of a rotation of 180° of the rotation axis x about its reference axis y and a contemporaneous translation of the rotation axis x along the reference axis y. Furthermore, the rotation axis x is at an angle with respect to the reference axis y by an angle a/2, in such a way that the rotation axis x is parallel to normal z, when the support element (130) is in the retracted configuration, and it is at an angle a with respect to normal z, when the support element (130) is in the extended configuration, and therefore the rotation axis x is always orthogonal to the surface (200).