I'm not sure what type of equations you need, but I believe you can find the equations you're looking for in my thesis on gear mechanism design
https://www.linkedin.com/posts/mehmet-berkay-yalt%C4%B1rakl%C4%B1-7449221b8_di%C5%9Fli-kutusu-tasar%C4%B1m%C4%B1-optimum-g%C3%BC%C3%A7-aktar%C4%B1m%C4%B1-activity-7074892437105590272-Zl9E?utm_source=share&utm_medium=member_desktop
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