Exponential submanifolds: A new kinematic model for mechanism analysis and synthesis

This paper aims to develop a new kinematic model, the exponential submanifolds (EXPSs) e^Ω with Ω a subspace of se(3) (the Lie algebra of the special Euclidean group SE(3)), for mechanism analysis and synthesis. The EXPSs provide perfect models for many global motion types appearing in the past mechanisms, robotics and kinesiology literatures which cannot be modeled as the well known Lie subgroups or their product. We derive in this paper both the sufficient and necessary conditions on Ω such that e^Ω is an EXPS, and geometric properties of the EXPS for mechanism analysis and synthesis.