for 200 USD I need a consultant to calculate the proper contact ratio for two gears for my project.

I am trying to keep an earbud expanded in an ear. I need to know the math behind the friction caused by the expansion. I need to have gears that will not lose rotational progress while holding the expansion in the ear canal. I appreciate it. Please message me in chat on freelancer how you are competent at the aspects of this job. I need to believe you are the right hire for this job. If I cannot gain the confidence then we will be wasting our time with me hiriing you.