 Dual quaternions have been used to exhibit transformations in the Euclidean group.A typical element can be written as a screw transformation.A benefit of the dual quaternion formulation of the composition of two spatial displacements "D""B" = (["R""B"], b) and "D""A" = (["R""A"],a) is that the resulting dual quaternion yields directly the screw axis and dual angle of the composite displacement "D""C" = "D""B""D""A".