Kinematic Singularities of Robot Manipulators

Abstract

The analysis of manipulator singularities is a burgeoning area of research. This chapter has touched briefly on some key themes. There are significant open problems, including understanding over-constrained mechanisms, genericity theorems for manipulator architectures, higher-order analysis and topology of the singularity loci, singularities of compliant mechanisms, bifurcation analysis and many more. The practical problems of manipulator design and control remain central goals, but their resolution involves many branches of mathematics including algebraic geometry, differential topology, Lie group theory, geometric algebra, analysis, numerical methods and combinatorics.