A yarn-clamping device for clamping yarns of a yarn layer (L1, L2), this device including - a clamping rail, which delimits a clamping volume extending along a longitudinal axis, - a clamping rod, configured to be inserted into the clamping volume through an insertion/extraction opening of the clamping rail and in a direction transverse to the longitudinal axis, a longitudinal portion of the clamping rod received in the clamping volume having a non-circular cross-section, the clamping rod having a clamping rotation movement relative to the clamping rail, in a clamping direction, within the clamping volume and around a rotation axis parallel to the longitudinal axis of the clamping rail, ∘ from an insertion position, where a first external dimension of the clamping rod cross-section, parallel to a width of the insertion/extraction opening, is smaller that this width, so that the rod can pass through the insertion/extraction opening, ∘ to a clamping position, where the clamping rod clamps the yarns located in the clamping volume against an internal surface located inside the clamping rail, characterized in that - with regard to a main plane of the clamping volume containing the rotation axis and crossing the insertion/extraction opening in the middle of this opening, one side of the clamping volume is delimited by the clamping rail and the other side of the clamping volume is partially delimited by an internal surface which belongs to a rubber profile housed in the clamping rail; - when the clamping rod is in the clamping position, the clamping rod penetrates the internal surface of the rubber profile, with the yarns in-between; and - when the clamping rod is in the clamping position, a maximum external dimension (d24, D1) of the clamping rod cross section, parallel to the width of the insertion/extraction opening, is strictly larger than the width of the insertion/extraction opening, the maximum external dimension (d24, D1) of the clamping rod cross section and the width of the insertion/extraction opening being measured at the same longitudinal level, along the rotation axis. - a clamping rail, which delimits a clamping volume extending along a longitudinal axis, - a clamping rod, configured to be inserted into the clamping volume through an insertion/extraction opening of the clamping rail and in a direction transverse to the longitudinal axis, a longitudinal portion of the clamping rod received in the clamping volume having a non-circular cross-section, the clamping rod having a clamping rotation movement relative to the clamping rail, in a clamping direction, within the clamping volume and around a rotation axis parallel to the longitudinal axis of the clamping rail, ∘ from an insertion position, where a first external dimension of the clamping rod cross-section, parallel to a width of the insertion/extraction opening, is smaller that this width, so that the rod can pass through the insertion/extraction opening, ∘ to a clamping position, where the clamping rod clamps the yarns located in the clamping volume against an internal surface located inside the clamping rail, ∘ from an insertion position, where a first external dimension of the clamping rod cross-section, parallel to a width of the insertion/extraction opening, is smaller that this width, so that the rod can pass through the insertion/extraction opening, ∘ to a clamping position, where the clamping rod clamps the yarns located in the clamping volume against an internal surface located inside the clamping rail, - with regard to a main plane of the clamping volume containing the rotation axis and crossing the insertion/extraction opening in the middle of this opening, one side of the clamping volume is delimited by the clamping rail and the other side of the clamping volume is partially delimited by an internal surface which belongs to a rubber profile housed in the clamping rail; - when the clamping rod is in the clamping position, the clamping rod penetrates the internal surface of the rubber profile, with the yarns in-between; and - when the clamping rod is in the clamping position, a maximum external dimension (d24, D1) of the clamping rod cross section, parallel to the width of the insertion/extraction opening, is strictly larger than the width of the insertion/extraction opening, the maximum external dimension (d24, D1) of the clamping rod cross section and the width of the insertion/extraction opening being measured at the same longitudinal level, along the rotation axis.