Hi, The mechanism connected to the shaft produces 111.404N of force with a time interval of 2 to 4 seconds. The displaced distance of the mechanism connected to the shaft is 0.8605meters, therefore the power produced varies from 47.93 Watts to 19.174 Watts. The gearing box needs to have a maximum diameter of 3.8cm. Could someone tell me how to find out the maximum gear ratio or guide me with how to do it, or other information I need to consider. I do not have a specific number of teeth, distance of depth I want to have between the gears. As long as I am able to maximize the gearing ratio it will be the best.Any guidance, answers, or anything in general will be highly appreciated. Please help. 
I didn't find the right solution from the Internet. 
References: https://www.engineersedge.com/engineering-forum/showthread.php/5239-Gearing-Ratio-Question Blockchain digital marketing 
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