This motorized carriage for opening/closing a curtain is able to move along a rail thanks to a friction wheel driven by an electric motor and pivot mounted in a casing containing this electric motor. The casing is provided with at least two members for suspending it from the rail or from the rod, which include a support and/or a base element and at least one pivoting roller. The casing is equipped with at least one housing for partially accommodating and reversibly immobilizing each suspension member, so that the pivoting rollers or the shoes of the suspension members are mounted removably on the casing. The support is mounted, removably and via a rotational movement (F4), in the housing. Elements allow the support to be immobilized about its axis of rotation. The movement assembly (E) includes a casing and at least two sets of two suspension members.