Apparatus for supporting and guiding a machine for operating on sheet material such as cloth while the material lies on a surface of a supporting structure having a pair of substantially parallel sides extending lengthwise of the structure, the apparatus comprising a carriage adapted for movement lengthwise of the supporting structure along a path substantially parallel to the sides, a guide arm on the carriage extending across the supporting surface between the sides and spaced from the surface, and a support arm connected to the guide arm extending at an angle thereto and located in spaced relation to the supporting surface, the support arm carrying at one end a machine for operating on the sheet material, and the support arm being pivotally movable about an axis substantially parallel to the longitudinal axis of the guide arm and along a plane disposed substantially perpendicular to the supporting surface. The support arm also is movable longitudinally along the guide arm and also is pivotally movable about an axis substantially perpendicular to the longitudinal axis of the guide arm. The support arm extends crosswise of the support arm and carries a balancing weight on the other end, and the balancing weight can be provided by another machine carried on that end of the arm. The machine can be provided with an improved supporting base characterized by a sheet of resilient material such as spring metal having an intermediate portion shaped to be spaced from the supporting surface, a leading edge portion contacting the surface and a trailing edge portion shaped to facilitate movement of the resilient sheet over and along the work surface.