How to select speed reduction ratio

I need to purchase a strain wave gear to reduce speed and increase torque in my motor. How to I find the ideal reduction ratio for the gear?

Regardless of what type of gearing you use, the gear ratio is what ultimately determines the output RPM and output torque. The “ideal” ratio is whatever output you need in terms of RPM and torque. For example if you need 10Kg-cm of toque, and the motor (without gearing) can provide 0.43Kg-cm, you would need a gear ratio of 10/0.43 = 23.36:1. The rpm would decrease by a factor of 23.36:1 as well. If this does not answer your question, can you provide some details? Also, why strain wave as opposed to cycloid or standard harmonic?

[size=2]I was under the impression that if there is too much speed reduction, the motor may have plenty of torque but the RPM will be too slow. If there is insufficient speed reduction, the motor will need to draw much more current than would otherwise be necessary to produce the required torque.[/size]
[size=2]And if the reduction is insufficient, the motor may be forced to work in an RPM range that is far from the speed at which it has high efficiency. This can cause overheating at relatively low levels of torque.[/size]
[size=2]Therefore, do I need to take into to consideration the peak efficiency of the motor before choosing a reducer.[/size]

[size=2]I thought harmonic drives and strain wave drives were the same thing. Also, are there any benefits of using cycloid over harmonic/strain wave. [/size]

Correct

Basically correct as well.

Not quite sure I understand that part.

Choose a motor with a gear reduction which provides the torque and RPM you need and then operate it at nominal voltage to get the highest efficiency.

“Harmonic drive” seems to be a brand name, much like “Kleenex”. These are still far less common than spur or planetary gearing.