Gordon,

A Worm/Worm-Gear set is, essentially, a *Trapezoid Thread* screw driving (or, occasionally, being driven by) a *Spiral Spur Gear*. In a *Spur Gear* the OD of the gear is the *Pitch Diameter* + 2/*Diametral Pitch* of the gear. Thus, the *driven area* of a *Spur Gear* is 4/*Diametral Pitch*. The *Root Diameter* of said *Spur Gear* has an additional clearance of .3125/[Diametral Pitch[/i] below that (*Root Diameter* = *Pitch Diameter* - 2.3125/*Diametral Pitch*). The *Pressure Angle* of the *Involute Tooth* you are using will be half the *included angle* of your mating *Trapezoid Thread*.

The *Pitch Diameter* of the *Trapezoid Thread* should be located 2/*Diametral Pitch* below the *Major Diameter* of the *Worm*. The *Minor Diameter** of the **Worm* should (in classical definition) be located 2.25/*Diametral Pitch* below the *Pitch Diameter* giving you a *thread depth* of 4.25/*Diametral Pitch* for your *Trapezoidal Thread*. [You **really** want to use *wires* to measure the *Pitch Diameter* and *Pitch* of your *Trapezoidal Thread*.]

The *Tooth Width* on your *Spur Gear* is *Pitch Diameter**sin(180/*Number of Teeth* (+0/-*Clearance*) on the *Pitch Diameter*. This is **also** the *Thread Width* and *Thread Spacing* (though the *Spacing* tolerance will be +*Clearance*/-0) to define the *per Revolution Pitch* from which the *Spiral Angle* for the mating *Spur Gear* may be calculated.

Does this help?