the u of the insert 12 has a cross section similar to that of fig3 with two partitions in a right angled cross one of the partitions being parallel to the running plane p the other partition being orthogonal to this plane fibers of the composite material which make the connection with the pivot 5 have been depicted diagrammatically in fig2 passing through the lower end of the pivot 5 is a hole 13 the axis of which is orthogonal to the axis x u2014 x and which lies in the mid plane p of the forks this hole 13 houses an embedded nut for a break calliper support spindle the insert 12 has two branches 14 a 14 b pointing downward and connected by the base of the inverted u each branch 14 a 14 b has a cavity which is open at the bottom and in which the corresponding end 15 of a corresponding fork blade core is engaged each core is surrounded by a layer of composite material 16 enveloping the insert 12 including the base which connects the branches 14 a 14 b the pivot 5 equipped with the insert 12 is assembled with the blades of the fork in a subsequent operation it would however be possible to manufacture the entire forks with pivot insert fork blades and dropouts in a single operation the pivot 5 is advantageously manufactured around a mandrel 17 fig4 for example a metal mandrel which has two longitudinal diametral slits 18 19 at right angles along part of its length the mandrel 17 comprises a cylindrical body 17 a equipped at its right hand end according to fig4 with a handle 20 the cylindrical body 17 a is extended toward the left.