Systems and methods are provided for gripping of a workpiece with a layer jamming structure having rigid datum structures. A system includes a layer jamming structure configurable in an inactivated conformable state, with a membrane defining an internal cavity containing a number of overlapping material layers. The rigid structures engage the layer jamming structure. A pressure system includes a pump coupled with the internal cavity to change a pressure therein to transform the layer jamming structure from the inactivated conformable state to an activated rigid state disposed around the workpiece. The rigid structures help conform the layer jamming structure to the workpiece during transformation to the activated rigid state and to present datum fixturing surfaces in the activated rigid state.