Cartan Connections as a Tool for Kinematic Chain Calculation

In this paper, the application of the concepts of Cartan connection and covariant derivative to robotics and mechanisms is presented. In particular, how Cartan connection can be used in kinematic calculation for rigid serial manipulators. The ideas were inspired in books of differential geometry, Lie groups and Lie algebras and its applications. The important concept of extended Newton’s law (or covariant formulations of dynamics) is also presented. It is presented first for the case of pure rotations and then for general motion of the robot’s links. Some calculations are presented for the case of a two-link planar robot, which is an example of serial mechanism, and for a planar n-bar mechanism, which is a closed-loop system. Finally, conclusions and future work directions are presented.