We extend our previous discussion ͓D. L. Keeling et al., Phys. Rev. Lett. 94, 146104 ͑2005͔͒ of molecular rolling on reactive surfaces. Experimental results showing long-range quasiperiodic tip responses with periods of two, three, and four lattice constants are presented. In addition, we show systematic change of the repeating wave form which we attribute to a slow variation of the tip-sample junction at an atomic level. Using ab initio simulations, we have reexamined the translation of C 60 across the surface and confirmed our proposed pivoting mechanism via which the molecule rolls by sequential breaking and forming bonds with the surface. A complex character of the molecular displacement, which is accompanied by a substantial deformation of the molecule and the surface, is revealed by careful analysis of the atomic geometry and the electron density redistribution along the path. A large variety of observed tip traces along the trough are then explained by analyzing in detail all possible transition paths between the known stable adsorption sites. Detailed models for the periodic traces with two and three lattice constants are also suggested based on a modified pivoting mechanism. In addition, we predict and discuss possible along-the-row manipulation paths.