Calculation of involute gears (center distance, profile shift, pressure angle, etc.)

In this video, we derive the basic formulas for calculating involute gears. We will mathematically determine the following parameters:

center distance, tip shortening, sum of the profile shift coefficients to obtain a certain center distance, operating pressure angle, transmission ratio, standard reference pitch circle, operating pitch circle, tip, root and base circle diameter, tip tooth clearance, (tip) tooth thickness, contact ratio

Here is the link to the Excel spreadsheet for calculating these parameters:

https://www.tec-science.com/wp-conten...

00:00 Construction of an involute
01:03 Definition of the involute function
02:00 Involute angle and pressure angle
02:51 Calculating the circular tooth thickness
04:52 Calculating the involute angle alpha (pressure angle)
06:48 Calculating the tip and root circle diameter
08:03 Calculating the reference circular pitch and base pitch
09:58 Calculating the operating pressure angle
12:36 Calculating the operating pitch circle diameters
13:37 Calculating the center distance
13:57 Calculating the profile shift coefficients (for a given center distance)
15:21 V-plus gearbox, V-minus gearbox, zero-gearbox (standard gearbox)
16:24 Tooth tip clearance
18:03 Calculating the tip shortening
19:47 Line of action & line of contact
20:55 Calculating the contact ratio
23:29 Excel spreadsheet for calculation