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Old Dec 17th 2017, 11:18 AM   #1
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Can anyone help me solve this problem related to gear trains

Im trying to solve this problem but just not getting it. Below is the problem.

An epicyclical gear train has a fixed annular wheel C concentric with sun wheel A. A planet wheel B gears with A and C and can rotate freely on a pin carried by an arm D which rotates about an axis coaxial with that of A and C. If TA and TC are the numbers of teeth on A and C respectively, prove that the ratio of the speeds(rpm) of D to A is equal to the ratio of TA to ( TA + TC)

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Old Dec 18th 2017, 03:58 PM   #2
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I think I must be missing something...

Assume that A is driven clockwise and C is held stationary

For every tooth's worth of rotation of A, B must also rotate by a tooth, which will cause it to push back against C, moving it anti-clockwise.

Note that every tooth's worth of rotation of A will cause B to move back One tooth's worth against C.

For B to move a full circle round the inside of C, the number of teeth's worth of rotation of B, and thus also the number of teeth's worth of rotation of A must equal the total number of teeth in C.

Thus for one rotation of D, A must rotate TC/TA times.

This is close to your desired answer, but...
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Old Dec 18th 2017, 04:06 PM   #3
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I think I see it

For every tooth's movement of A clockwise, B will move a tooth's worth anticlockwise with respect to C,
But that will also mean it will move a tooth's worth anticlockwise with respect to A.
Thus after a full rotation round C it must have also made a full additional rotation about A.

Lots of words and a difficult mental visualisation, I hope it helps
(rather than just confusing further).
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Old Dec 19th 2017, 02:32 AM   #4
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Oops

I thought someone would have jumped in and corrected me.

For every tooth's movement of A clockwise, B will rotate anticlockwise which will move it a tooth's worth clockwise with respect to C.

I think the rest stands
(but don't just trust me, check it for yourself).
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