| The PDF document that was removed from the http://tco.gsfc.nasa.gov/tops/CVPT.pdfaddress described a «Continuously Variable Planetary Transmission» that claimedbeing a Geared CVT. | |
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Lets calculate the angular velocity of the planet-axis in two cases. |
1st case: |
1st case: Consider the ring gear meshed with the large diameter section of the beveledplanetary gear, as shown on the left.
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For calculations purpose, consider the planetary axis (P) motionless.
If the sun gear (A) rotates with angular velocity NA=X, then the planet B
wouldrotate with angular velocity So, the ring gear (D) would rotate with angular velocity ND=NC*C/D, Thus, multiplying, ND=X*((A*C)/(B*D)). |
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Now consider the real case: the ring gear is motionless. In order to
mantain the same relative motion between gears, we will have to add
angular velocities.
Thus, ND=0 => (NP1 is the angular velocity of point P in case1) <=> X=NA*(1+((A*C)/(B*D))) ; Thus,
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2nd case: |
2nd case: Consider the ring gear meshed with the small diameter section of the beveledplanetary gear, as shown on the left. Doing similar considerations, we would obtain: (NP2 is the angular velocity of point P in case2) |
| Before the final step, we must remember that, the perfect
meshing of the ring gear with the planet gears requires equal pitch. The beveled planetary gears have smaller pitch on the smaller diameter, say pitch2. And pitch1 on the bigger diameter. When the ring gear is in case1 the ring gear must deform to pitch1, and when it's on case2, pitch2. Either the planet or the ring gear have a fixed number of teeth. Thus their diameter must be proportional to their common pitch. So, pitch1/pitch2=C/E=D/F. Thus, the angular velocity of point P is the same in both cases. And
the tangential velocity of the spur gears (concentric with the planets)
will not vary. So, the output speed of this CVPT transmission is the same,
in both cases.
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