Involute splines...

Excuse my ignorance, but I have the Diametrical pitch, No of teeth, pressure
angle, and spline OD for a internal spline cut, to hook to a hydraulic
motor. I have refered to the machinist handbook and for the most part dont
get it... HELP! How do I model this cut or is there some toolbox part I can
use, or some rule of thumb, some parametric model I can use.... Anything?
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Ben Eadie
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The short answer is search the newsgroup. But since I am a fan of involute construction methods here goes:
1. The approximate method involves creating a polygon with 360 sides. Starting at one of the vertices sketch a small arc that contacts the base circle and extend out from it. Then from the next vertex over construct a small arc tangent to the first. From the next vertex do the same till you have enough of the involute to define a tooth.
2. You will find the equations you need here:
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Given the pitch diameter the square root of the sum of the squares of the equations for X and Y at t=20deg (in radians) will give an equation you can solve for a, the base diameter.
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See model at , file "".
Pitch diameter and pressure angle work to produce the base diameter from which the involute starts. From there, the involute is determined by where the endpoint of a string would be as it is unwrapped from the base diamater.
In this model, I use P.D. and pressure angle to get the base diameter.In 5 degree increments, I "unwrap" the string curves to get points on the involute by constraining the tangent straight line length equal to the arc length in each of the construction sketches. The resulting points are mirrored tominimize curvature straightening at the base of the involute.
Still not a methematically "true" involute, but it was used to cut a gear that's been in service for two years now.
Ben Eadie wrote:
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This site has inexpensive involute spline generating software. Output is .dxf. Our company has a license. It takes a little practice, but works well.
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