This thesis investigates a general class of mechanism configurations, usually referred to as kinematic singularities. The study of such configurations is of major practical and theoretical importance. Indeed, the kinematic properties of mechanisms change significantly in a singular configuration, and these changes can prove to be either beneficial or undesirable for different applications. On the other hand, the theoretic significance of singularities in mechanism theory is well-known and related to the fact that singular points play a prominent role in the theory of differentiable mappings.

The central objective of this dissertation is to address the problems of mechanism singularity in a most general setting, namely, to consider arbitrary singular configurations of both non-redundant and redundant mechanisms with arbitrary kinematic chains, with a special emphasis on the study of mechanical devices with complex kinematic chains and non-serial, high-degree-of-freedom architectures. To this goal, a rigorous general mathematical definition of kinematic singularity for arbitrary mechanisms is introduced. This is achieved by means of a mathematical model of mechanism kinematics formulated in terms of differentiable mappings between manifolds. When the mathematical model is applied to the relationship between the joint and output velocities, a new unifying framework for the interpretation and classification of mechanism singularities is obtained. This framework, based on the newly introduced six singularity types, is applicable to arbitrary non-redundant as well as redundant mechanisms. Mathematical tools, such as singularity criteria and identification methods, are developed for the study of the singularity sets of both non-redundant and redundant systems with lower kinematic pairs.