Quotient kinematics machines: Concept, analysis and synthesis

In this paper, we identify a class of structurally distinguished machines, called quotient kinematics machines (QKM). A QKM realizes a motion task, typically characterized by a subgroup G of rigid transformation group SE(3), through coordinated motion of two mechanisms called modules. One is referred to as a subgroup module H and the other a complementary or quotient module G/H of H in G. Since QKM can retain both large workspace/rotation range of SKMs and speed/accuracy of PKMs by appropriate choice of modules, it is often implemented in high end machine design for semiconductor die/wire-bonding and 5-axis machining, etc. To promote QKM technology beyond occasional studies and applications, we use differential geometric techniques to develop a rigorous and precise treatment of QKMs, including: (i) modeling and analysis of QKMs; (ii) classification and synthesis of QKMs; (iii) PKM realization of quotient modules.