  Discrete and periodic contact switching is a key characteristic of
steady-state legged locomotion. This paper introduces a framework for modeling
and analyzing this contact-switching behavior through the framework of
geometric mechanics on a toy robot model that can make continuous limb swings
and discrete contact switches. The kinematics of this model form a hybrid
shape-space and by extending the generalized Stokes' theorem to compute
discrete curvature functions called \textit{stratified panels}, we determine
average locomotion generated by gaits spanning multiple contact modes. Using
this tool, we also demonstrate the ability to optimize gaits based on the
system's locomotion constraints and perform gait reduction on a complex gait
spanning multiple contact modes to highlight the method's scalability to
multilegged systems.
