Quotient kinematics machines: Concept, analysis and synthesis

In mechanism and machine design, the notion of serial kinematics machine (SKM), parallel kinematics machine (PKM) and hybrid kinematics machine (HKM) is well understood. In this paper, we introduce a fourth type of kinematics machine, known as quotient kinematics machine(QKM). A QKM generating a subgroup motion G consists of two mechanisms (or motion modules) acting in unison, one synthesizing a subgroup H of G, and another that of a complement of G/H. Apparently, the two motion modules of a QKM have simpler kinematic structures than that of a SKM, PKM or HKM with the same motion type G, and thus is expected to have performance advantages in terms of stiffness (speed and accuracy), modularity and etc, over its SKM/PKM/HKM counterparts. The formulation of the QKM concept and its analysis and synthesis are considered in this paper.