Our lever arm corkscrew did not come with a stand, so I made one. The metal pin on the corkscrew sits in an 8.2mmØ hole. The first design I made (CorksrecStanSimple) supports the corkscrew in a horizontal position, but does not hold the arms together.
The second design (CorkScrewStand2), shown in the photos, hols the corkscrew at a 20° angle and holds the arms together, taking up less space and leaving less opportunity for the thing to fall over.
This design also afforded me the opportunity to use the blend (loft) tool, finally introduced into DesignSpark software.