A conformal vacuum cup (10) provides a machine tool attachment fitting usable in a flexible-track drill system. Using multiple, independently articulated stiffeners (26,28), the conformal vacuum cup conforms to the contour of complex aerostructure surface shapes (70). The individual stiffeners are decoupled from each other to some extent by grooves (62) and slots (60) molded into resilient overmolding material to support long-axis curving. Spacing pins (18) employ a domed shape consonant with the elastic deformation of the workpiece surface (70) under load. The pins (18) employ a hard material to prevent particle embedment in use and to control position tolerance for drill heads and other tools traveling on the flexible track. Partial holes (24,54) in each vacuum cup are blocked by diaphragms (58). Interconnection from a vacuum system manifold to the vacuum cups can be realized by penetrating the diaphragms and inserting barbed fittings (64) connected by vacuum tubing (68).