Why is the addendum of the gear kept equal to the module?

[Divya Shyam Singh]

In general calculations of gear design, addendum is taken as a factor of the module of the gear such as equal to module or 0.8 times the module and dedendum is taken as 1.25 times the module. Why are both these defined in terms of module? How did we reach to this conclusion?

 

[DaveC426913]

I have yet to find a single diagrammatic reference to the module of a gear. Every diagram I look at shows the addendum and dedendum with reference to the pitch cicle.

 

[DaveC426913]

Apropos of nothing, I wonder if this geometry explains why the discrepancy between addendum=0.8 and dedendum=1.25

 

[Divya Shyam Singh]

Section 3.2
"To reduce the varieties of gears to a manageable numbers, standards are evolved. Standard makes it easy for design, production, quality assurance, replacement etc. Three commonly used pressure angles are 14.5o , 20o and 25o pressure angle systems as shown in Fig. 3.3. In this, one can have full depth gears or stronger stub tooth gears. In Standard tooth system for metric gears, addendum: a =1m, dedendum: b= 1.25m where as the for the stub tooth gears, addendum a = 0.8m and dedendum: b= 1.0m. The shorter tooth makes it stronger and its load carrying capacity increases. It also helps in avoiding interference in certain cases"
Source: http://nptel.ac.in/courses/112106137/pdf/2_3.pdf

I have also read this in a number of machine design handbooks. But still i don't understand how did they reach that factor. Was it an experimental result? or perhaps some analytical model...?