How to analyse a gear problem in mechanics of machines?
Depends on what your problem is. If you go to your local library, you
should be able to find a machine design book that will have an entire
chapter on gear design. In it will be terminology, equations, etc. that
should help you analyze just about all gear problems. You can also find
some general information in a book called "Machinery Handbook". The
Machinery Handbook gives some generalized equations and "rule" you should
follow in designing gears.
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Update: June 2012