Quaternion position representation in robot kinematic structures

This paper presents a full background of the two conventions for the quaternion position representation. One convention is corresponding with the column vector convention of homogeneous transformation matrices. A second convention is corresponding with the row vector convention of homogeneous transformation matrices. The matrices and vectors used in the two different conventions are simply transposes of each other. The aim of the paper is to show the composition of quaternion pairs used in the two different conventions.