Static Stability of Planar Contacting Systems: Analytical Treatment in Euclidean Space

This paper gives an exact theory in Euclidean space for studying the static stability of planar rigid systems held by one or more frictional and frictionless contacts under gravity. Static stability analysis deals with determining the feasible locations of the Centre of gravity (CG) which ensure stability. The analysis is performed here in two steps- finding the equilibrium region and finding the stability region as a subset of the equilibrium region. The stability region is determined through the analytical treatment of an elegant geometric characterization. These results are also verified through elegant geometric reasoning based on curvature theory in-plane kinematics. In the end, stability analyses of some physical systems containing generic contacting curves are il- lustrated and the results are presented with physical interpretations.