This paper traces the work back to the time when Rodrigues parameters were discovered and follows the theoretical development of rigid body displacements from the early 19th century to the late 20th century. The paper reviews the work from Chasles motion to Cayley’s formula and then to Hamilton’s quaternions and Rodrigues parameterization and relates the work to Clifford biquaternions and to Study’s dual angle proposed in the late 19th century. The review of the work from these mathematicians concentrates on the description and the representation of the displacement and transformation of a rigid body, and on the mathematical formulation and its progress.
The paper further relates this historic development to the contemporary development of the finite screw displacement and the finite twist representation in the late 20th century.