All Minor-Minimal Apex Obstructions with Connectivity Two

A graph is an apex graph if it contains a vertex whose deletion leaves a planar graph. The family of apex graphs is minor-closed and so it is characterized by a finite list of minor-minimal non-members. The long-standing problem of determining this finite list of apex obstructions remains open. This paper determines the $133$ minor-minimal, non-apex graphs that have connectivity two.

Bending Stress in Gear Teeth Having Circular Arc Profiles—Part 1: Analysis

The bending stress in the root fillets of gear teeth having convex, circular-arc profiles has been calculated using a new analytic model. The gear tooth is modeled as a wedge with the load applied at the apex. Graphs of the nondimensional bending stress variation along the tooth length are presented for 14.5 deg, 30 deg, and 47.5 deg normal pressure angle, and 5 to 45 deg helix angles. It is shown that gears with larger helix angles have higher bending stresses for the same value of allowable surface stress.