This experiment explored the effects of controlled manipulations of three parameters of tactile gratings, groove width (1.07-2.53 mm), contact force (30-90 g), and scanning speed (40-120 mm/s), on the responses of cells in second somatosensory cortex (SII) of awake monkeys that were performing a groove-width classification task with passively presented stimuli. A previous experiment involving an active touch paradigm demonstrated that macaque SII cells code groove-width and hand-movement parameters in their average firing rates. The present study used a passive-touch protocol to remove somatosensory activation related to hand movements that accompany haptic exploration of surfaces. Monkeys maintained a constant hand position while a robotic device delivered stimulation with tactile gratings to a single stabilized finger pad. Single-unit recordings isolated 216 neurons that were retrospectively assigned to SII on histological criteria. Firing patterns for 86 of these SII cells were characterized in detail, while monkeys classified gratings as rough (1.90 and 2.53 mm groove widths) or smooth (1.07 and 1.42 mm groove widths), with trial-wise random, parametric manipulation of force or speed; the monkeys compared 1.07 versus 1.90 mm and 1.42 versus 2.53 mm in alternating blocks of trials. We studied 33 cells with systematic variation of groove width and force, 49 with groove width and speed, and four with all three variables. Sixty-three cells were sensitive to groove width, 43 to force (effects of random force in speed experiments contributed to N), and 34 to speed. Relatively equal numbers of cells changed mean firing rates as positive or negative functions of increasing groove width, force, and/or speed. Cells typically changed mean firing rates for two or three of the independent variables. Effects of groove width, force, and speed were additive or interactive. The variety of response functions was similar to that found in a prior study of primary somatosensory cortex (SI) that used passive touch. The SII sample population showed correlated changes (both positive and negative) in firing rates with increasing groove width and force and to a lesser degree, with increasing groove width and speed. This correlation is consistent with human psychophysical studies that found increasing groove width and force increase perceived roughness magnitude, and it strengthens the argument for SII's direct involvement in roughness perception.