I have a problem that has so far stumped our small project engineering staff. I have a gear train that comprises a pinion (pinion 1) that meshes with two idlers (idlers 1 & 2), that in turn mesh with an internal gear. Another pinion (pinion 2) also meshes with idler 1. Both idlers mesh with the same internal gear. The idlers, pinions, and internal gear have fixed centers. Pinion 1 drives idler 2, and Pinion 2 drives idler 1. Both idlers drive the internal gear. The internal gear is an arc segment. Due to space issues, idler 1 can become disengaged from the internal gear at extreme travel, so Pinion 1 is meshed with Idler 1 to provide timing of idler1 so idler 1 can mesh with the internal gear on return. We would like to split drive torque from the pinions to internal gear through the idlers, so don't want pinion 1 to transmit torque to idler 1. Therefore, our desire is to have greater backlash between pinion 1 and idler 1 than between pinion 1 and idler 2. Backlash between the idlers and internal gear are the same. We are pretty sure this can be done by altering the positions of pinion 1 and idler 2. We can mathematically determine the gear centers with equal backlash, but are scratching our heads about how to do it with unequal backlash. Is there a mathematical way, either closed or iterative, to determine the theoretical positions of the idlers and pinion for this configuration, or can it only be accomplished through trial and error? I have a sketch of the gear configuration that I can email, if desired. Thanks for any help you can give.
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