I would like to make gears, but I need to know the tooth shape in order to make a form tool or cut an outline. This is what I came up with, if there are any mistakes or bad assumptions, please let me know.
I referenced: http://en.wikipedia.org/wiki/Gear http://en.wikipedia.org/wiki/Involute_gear http://en.wikipedia.org/wiki/Involute http://en.wikipedia.org/wiki/Rack_and_pinion My example gear is a 2m(module) pitch - 20mm. A sample is on this page: http://www.qtcgears.com/RFQ/default.asp?Page=../KHK/newgears/KHK044.html (Short URL) http://alturl.com/whp2 Pitch is the tooth length, but expressed in pitch circle diameter, so a 10 tooth gear with a 20mm pitch circle = 20mm/10t = 2, but this is not the linear tooth length. I believe the basis for involute gears is the trapezoidal rack, so I need the linear tooth length, which should be 2 module x pi. A common pressure angle is 20 degrees. I assumed the rack base and top are horizontally midway between the rack center line and the 20 degree peaks, such that the X length of the rise, flats and falls are equal. Here is my rack and pitch circle: http://www.wallacecompany.com/machine_shop/gears/rack_and_pitch_circle.png (Short URL) http://alturl.com/7t8a The first pinion tooth form guess is the complementary shape of the rack tooth, but as the rack moves the pinion rotates and lifts, so the pinion tooth shape needs to change to take the trapezoidal shape that matches the rotation and lift. If I move the rack one quarter of a tooth the pinion will rotate a proportionate angle. 1/4t = 1.5708mm C = pi x D = pi x 20mm = 62.832mm = 360 degrees 360deg x 1.5708mm/62.832mm = 9 degrees per 1/4t If I move the rack shape 1/4t to the right, then rotate it 9 deg clockwise back to the home position, the mesh point will be somewhere on the new shape. http://www.wallacecompany.com/machine_shop/gears/rack_and_quarter_tooth.png (Short URL) http://alturl.com/gd75 If I continue the process, I'll have more mesh points. http://www.wallacecompany.com/machine_shop/gears/rack_and_pinion_shape.png (Short URL) http://alturl.com/54oj I can then trim the lines, mirror the shape on the tooth center line, guess at a tip and base clearance shape. http://www.wallacecompany.com/machine_shop/gears/gear.png (Short URL) http://alturl.com/cqcw The problem is, have I made any mistakes? Is there a better, easier way? -- Kirk Wallace http://www.wallacecompany.com/machine_shop/ http://www.wallacecompany.com/E45/index.html California, USA ------------------------------------------------------------------------------ The NEW KODAK i700 Series Scanners deliver under ANY circumstances! Your production scanning environment may not be a perfect world - but thanks to Kodak, there's a perfect scanner to get the job done! With the NEW KODAK i700 Series Scanner you'll get full speed at 300 dpi even with all image processing features enabled. http://p.sf.net/sfu/kodak-com _______________________________________________ Emc-users mailing list Emc-users@lists.sourceforge.net https://lists.sourceforge.net/lists/listinfo/emc-users
