Antennae are the main organs of the arthropod tactile sense. In contrast to other senses that are capable of retrieving spatial information, e.g. vision, spatial sampling of tactile information requires active movement of the sense organ. For a quantitative analysis of basic principles of active tactile sensing, we use a generic model of arbitrary antennae with two hinge joints (revolute joints). This kind of antenna is typical for Orthoptera and Phasmatodea, i.e. insect orders that contain model species for the study of antennal movements, including cricket, locust and stick insect. First, we analyse the significance of morphological properties on workspace and sampling acuity. It is shown how joint axis orientation determines areas out of reach while affecting acuity in the areas within reach. Second, we assume a parametric set of movement strategies, based on empirical data on the stick insect Carausius morosus, and investigate the role of each strategy parameter on tactile sampling performance. A stochastic environment is used to measure sampling density, and a viscous friction model is assumed to introduce energy consumption and, thus, a measure of tactile efficiency. Up to a saturation level, sampling density is proportional to the range or frequency of joint angle modulation. The effect of phase shift is strong if joint angle modulation frequencies are equal, but diminishes for other frequency ratios. Speed of forward progression influences the optimal choice of movement strategy. Finally, for an analysis of environmental effects on tactile performance, we show how efficiency depends on predominant edge direction. For example, with slanted and non-orthogonal joint axis orientations, as present in the stick insect, the optimal sampling strategy is less sensitive to a change from horizontal to vertical edge predominance than with orthogonal and non-slanted joint axes, as present in a cricket.