A headlamp comprising: - a support comprising a horizontal base and a fixing (202, 203) for a retaining strip; said support comprising two vertical lateral parts (210, 220), said vertical lateral parts (210, 220) comprising a first left lateral part and a second right lateral part; - a lamp body comprising a light source associated with electrical circuits for the electrical supply and the control of the light source, said lamp body being configured to be located between said first and second lateral parts (210, 220) and connected thereto by means of a mechanical connection combining a pivot function with a translation making it possible to maintain said lamp pivot, as and when the latter is pivoted, as close as possible to the horizontal base of the support; Wherein said first left lateral part comprises a first horizontal rod and a first curvilinear guide groove situated in the vertical plane of the first left lateral part and having an axis of vertical symmetry; - said second right lateral part comprises a second horizontal rod and a second curvilinear guide groove situated in the vertical plane of the second right lateral part and having a vertical axis of symmetry; - said lamp body has on a left side a third horizontal rod intended to cooperate with said first curvilinear guide groove of the left lateral part as well as a third rectilinear guide groove intended to guide in translation said first rod; - said lamp body comprises on a right side a fourth horizontal rod intended to cooperate with said second curvilinear guide groove in the right lateral part as well as a fourth rectilinear guide groove intended to guide in translation said second rod; whereby the guiding of said first and second rods (211, 221), respectively in said third and fourth rectilinear grooves, simultaneously with the guiding of said third and fourth rods respectively in the first and second grooves of curvilinear guides simultaneously ensure a translational and rotational movement of the lamp body making it possible to maintain the latter as close as possible to the base of the support.. - a support comprising a horizontal base and a fixing (202, 203) for a retaining strip; said support comprising two vertical lateral parts (210, 220), said vertical lateral parts (210, 220) comprising a first left lateral part and a second right lateral part; - a lamp body comprising a light source associated with electrical circuits for the electrical supply and the control of the light source, said lamp body being configured to be located between said first and second lateral parts (210, 220) and connected thereto by means of a mechanical connection combining a pivot function with a translation making it possible to maintain said lamp pivot, as and when the latter is pivoted, as close as possible to the horizontal base of the support; Wherein said first left lateral part comprises a first horizontal rod and a first curvilinear guide groove situated in the vertical plane of the first left lateral part and having an axis of vertical symmetry; - said second right lateral part comprises a second horizontal rod and a second curvilinear guide groove situated in the vertical plane of the second right lateral part and having a vertical axis of symmetry; - said lamp body has on a left side a third horizontal rod intended to cooperate with said first curvilinear guide groove of the left lateral part as well as a third rectilinear guide groove intended to guide in translation said first rod; - said lamp body comprises on a right side a fourth horizontal rod intended to cooperate with said second curvilinear guide groove in the right lateral part as well as a fourth rectilinear guide groove intended to guide in translation said second rod; - said second right lateral part comprises a second horizontal rod and a second curvilinear guide groove situated in the vertical plane of the second right lateral part and having a vertical axis of symmetry; - said lamp body has on a left side a third horizontal rod intended to cooperate with said first curvilinear guide groove of the left lateral part as well as a third rectilinear guide groove intended to guide in translation said first rod; - said lamp body comprises on a right side a fourth horizontal rod intended to cooperate with said second curvilinear guide groove in the right lateral part as well as a fourth rectilinear guide groove intended to guide in translation said second rod; whereby the guiding of said first and second rods (211, 221), respectively in said third and fourth rectilinear grooves, simultaneously with the guiding of said third and fourth rods respectively in the first and second grooves of curvilinear guides simultaneously ensure a translational and rotational movement of the lamp body making it possible to maintain the latter as close as possible to the base of the support..