Line-symmetric motion generators

When a rigid body is axially reflected through a moving line, its image undergoes a so-called line-symmetricmotion. The space comprising all possible line-symmetric motions that share a common initial line is a four-dimensional submanifold, denoted M4, in the special Euclidean group SE(3). Recently, we showed that M4 may be used to characterize motions of a line-symmetric body that are free of self-spin and sliding, thus lending itself to applications such as remote center of motion devices for minimal invasive surgery and haptic interfaces. Aiming at designing robot mechanisms for these applications, we present in this paper a systematic enumeration of line-symmetric motion generators (LSMGs), i.e., robot mechanisms that generate the line-symmetric motion manifold M4, following a procedure based on symmetric space theory. LSMGs present a ubiquitous line symmetry of their joint axes, thus offering a new understanding of the line-symmetric motions.