## 1 Introduction  
Four types of tactile mechanoreceptors mediate most of the sensation in human skin: [PERSON]'s disks, Meissner's corpuscles (MCs), Ruffini endings, and Pacinian corpuscles (PCs) [1; 2; 3]. These mechanoreceptors allow for various haptic sensations such as touch and pressure by [PERSON]'s disks, skin stretch by Ruffini endings, and vibration by [PERSON]'s and Pacinian corpuscles [1; 4; 5]. Haptic perception (touch and vibration) has been studied widely, leading to development of body-machine interfaces (BMI; [6; 7; 8; 9; 10; 11; 12; 13; 14; 15; 16; 17; 18; 19; 20; 21; 22; 23]) that can stimulate the skin electrically [7], pneumatically [8], or tacitely to provide performance feedback to users [9; 10; 11]. Tactile interfaces are by far the most popular, as they are relatively inexpensive to construct, non-invasive, and can be implemented at various locations on the body where skin sensation remains intact. Tactile stimulation can be implemented using vibrating elements [12; 13; 14; 15; 16; 17; 18], pressure [19; 20], or skin stretch [21; 22; 23]. Interfaces that use vibrotactile stimulations target [PERSON]'s corpuscles by delivering low-frequency stimulations (5-60 Hz) or Pacinian corpuscles with higher frequency stimulations (60-400 Hz) [2; 5; 24; 25]. With this wide bandwidth of stimulation frequencies available, vibrotactile interfaces can provide a large range of performance feedback information to the user. Our long-term goal is to advance the development of inexpensive and non-invasive BMIs that use vibrotactile interfaces attached to the arm to provide performance feedback to users. Many of these interfaces rely on a multi-channel setup that often use the 2-point touch discrimination threshold (2-TDT) to determine the distance between two stimulation sites. However, this distance may not accurately represent the physical space needed between two vibrotactile stimuli because touch and vibration activate different mechanoreceptors (i.e., [PERSON]'s disks and MCs/PCs, respectively). The 2-point distance for vibrotactile stimuli applied to the hand and fingers has been previously investigated [26; 27]. [PERSON] et al. found that the 2-point distance on the fingertip for high-frequency stimulations (500 Hz, using piezoceramic vibrating pegs) was more than two-fold higher, at 0.5 cm, than the 2-point distance for low-frequency stimulations (25 Hz) at 0.2 cm [26]. [PERSON] et al. found that at low-frequency stimulations (25 Hz, using a single probe tip) 2-point distance for the hand dorsum was approximately 0.5 cm [27]. Comparing the two studies, one can see that the 2-point distance changes with body location and vibration frequency. However, results of those studies are difficult to generalize to the skin of the forearm due to differences in mechanoreceptor densities between the glabrous skin of the hand and the hairy skin of the arm [3]. [PERSON] et al. used rotating mass vibration motors to investigate the perception of relatively high-frequency vibrotactile stimuli (122-156 Hz) on the volar forearm using three motors, spaced 3 cm apart [13]. [PERSON] et al. found that errors in spatial discrimination of vibrotactile stimuli were greater when stimuli were delivered by two motors spaced 3 cm apart compared to motors spaced 6 cm apart. [PERSON] and [PERSON] [28] used inter-motor distances of 2.5 cm on the arm and found vibration localization accuracy as low as 46% (i.e., people were inaccurate in localizing vibration stimuli when the inter-stimulus distance was small). [PERSON] and [PERSON] reported that the localization accuracy increased to 86% when the inter-stimulus site distance was increased to 5 cm. They concluded that interactions between the mechanical and physiological properties of the skin produced interference in vibrotactile localization. It is possible that mechanical propagation of vibration stimuli along the skin can negatively impact vibration perception as mechanoreceptors in the skin adjacent to the site of the vibration may also respond to the stimulus.