Braking and/or clamping assembly in a slide guided to move along at least one rail, - the assembly provided in a housing and comprising at least one frictional constraining means (51, 151) adapted to be operated through a wedge-actuated transmission (50, 150) and including at least one pressing piece (54, 154) adapted to be urged against the rail, and/or friction jaws (53, 153); - the members (45, 145, 54, 154, 71, 72, 91, 92) of said wedge-type transmission being moved by means of extraneous energy and being adapted to be moved by means of at least one actuator (60, 160) or by means of a spring system for loading and unloading each individual frictional constraining means (51, 151) per loading and unloading direction, said spring system comprising at least one spring element (88, 98); and - the wedge-type transmission (50, 150) including a least one cage, said cage movably mounted between at least one pressing piece (54, 154) and/or friction jaws (53, 153) and a least one housing-side rolling zone or a support element (45, 145) provided in the housing; characterized in that - the movable portion of the actuator (60, 160), including the longitudinal guide of the latter, defines a wedge angle of 0.2 to 5 degrees relative to the direction of slide displacement; - the housing-side rolling zone or the support element (45, 145) has an end face turned towards the cage (71, 72), said end face having therein at least in parts thereof a planar surface area or a channel oriented parallel with the direction of displacement of the movable portion of the actuator and/or of its guide; and - the pressing piece (54, 154) has a rolling surface area of which a line normal thereto or centre line is oriented perpendicular to the direction of slide displacement. - the assembly provided in a housing and comprising at least one frictional constraining means (51, 151) adapted to be operated through a wedge-actuated transmission (50, 150) and including at least one pressing piece (54, 154) adapted to be urged against the rail, and/or friction jaws (53, 153); - the members (45, 145, 54, 154, 71, 72, 91, 92) of said wedge-type transmission being moved by means of extraneous energy and being adapted to be moved by means of at least one actuator (60, 160) or by means of a spring system for loading and unloading each individual frictional constraining means (51, 151) per loading and unloading direction, said spring system comprising at least one spring element (88, 98); and - the wedge-type transmission (50, 150) including a least one cage, said cage movably mounted between at least one pressing piece (54, 154) and/or friction jaws (53, 153) and a least one housing-side rolling zone or a support element (45, 145) provided in the housing; - the movable portion of the actuator (60, 160), including the longitudinal guide of the latter, defines a wedge angle of 0.2 to 5 degrees relative to the direction of slide displacement; - the housing-side rolling zone or the support element (45, 145) has an end face turned towards the cage (71, 72), said end face having therein at least in parts thereof a planar surface area or a channel oriented parallel with the direction of displacement of the movable portion of the actuator and/or of its guide; and - the pressing piece (54, 154) has a rolling surface area of which a line normal thereto or centre line is oriented perpendicular to the direction of slide displacement.