Transference principle and its applications to the robots and manipulators

This principle with important applications in theory of mechanisms is formulated recently by Martinez, Duffy as: Any valid equation involving a finite product of differentiable quaternion functions remains valid when the dual mapping is aplied to both sides of the equation. Among the applications we remark the study of instantaneous invariants of rigid body motions to an iterative algorithm for the position analysis of spatial mechanisms. The principle of transference can be extrapolated via the corresponding isomorphisms to any Euclidean group that are related by the dualization mapping and is embedded into the Clifford algebras and dual numbers as example for dual Pauli spin matrices or dual unit quaternion. After geometrical extensions of this principle to screw systems the authors present its applications to a serial chain manipulator in a general fashion, respectively, the algorithms for direct and inverse computations.