This video shows DexTAR, a double-SCARA parallel robot, which is probably the best pedagogical example of a parallel mechanism. Both serial and parallel singularities are demonstrated. DexTAR crosses serial singularities (i.e., changes working modes) in order to enlarge its workspace. It can also cross parallel singularities, but the control strategies required to do so in an optimal way are very complicated. Besides, there is very little advantage of crossing parallel singularities (i.e., changing assembly modes).
