The weak interlayer binding in two-dimensional layered materials such as graphite gives rise to poorly understood low-friction characteristics. Accurate measurements of the adhesion forces governing the overall mechanical stability have also remained elusive. We report on the direct mechanical measurement of line tension and friction forces acting in sheared mesoscale graphite structures. We show that the friction is fundamentally stochastic in nature and is attributable to the interaction between the incommensurate interface lattices. We also measured an adhesion energy of 0.227 +/- 0.005 joules per square meter, in excellent agreement with theoretical models. In addition, bistable all-mechanical memory cell structures and rotational bearings have been realized by exploiting position locking, which is provided solely by the adhesion energy.