This reply to @Caleb's comment kept growing and growing into an off-topic answer. Maybe you still find it useful.

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After mounting the zoom ring gear, I'll attach a pinion gear to the stepper motor shaft to control the motion of the zoom ring.

A linear zoom throw allows for smooth, consistent zooming that doesn't draw attention to itself.

"stepper motor" and "smooth" don't go together well.

Stepper motors make steps (hence the name ;)) and never a continuous motion. There's no way around the fact that the torque (which is the thing that causes the motion) is applied in discontinuous steps. You can smooth the motion with various efforts to some degree, but such efforts take away the inherent advantage of the stepper motor: its simplicity. And even if you manage to smooth out the motion to a desirable degree, you basically created a regular motor, so why not use that in the first place?

Take a look at the various stabilising gimbals. They often use brushless motors. What would the footage look like if they used a ste-ep-ep-ep-epper motor instead?

And should you ever want to turn the motor driver off to allow manual rotation of the zoom ring, you'd always have to disengage the gear that connects the stepper motor mechanically to the lens, because the steps of a stepper motor are noticeable when rotating it by hand.

I don't like to be that guy, but to some degree your question reads like this:

There are these expensive lenses that have the properties A, B and C which all make them expensive to manufacture. Now I'd like to duct tape a stepper motor to a lens with the same properties and have it for cheap. Any ideas how?

I'm not seeing how merely requiring the existence of the same properties of an expensive lens enables you to build a cheap one.

It adds another layer of complexity. I would need to discover - either through research or (more likely) experimentation - the actual behavior of the zoom throw, which can be complex.

Chances are that lens companies do actually do some research and development. I'm afraid now it's your turn. You have some engineering to do that goes beyond "I just buy components that happen to full fill all my requirements".

I also don't need auto [...] focus

I think you do want auto focus, though, but not for auto focus in the classical sense. That's because automation of both zoom and focus enables you to control either one, but also both at the same time, depending on each other.

When you calibrate a lens, you obtain knowledge about how

• focus changes, depending on focal length (varifocus)
• zoom changes, depending on zoom ring rotation (nonlinearity of the ring)

Knowing these static errors, you can compensate for them during operation. As suggested by @Caleb in a comment, you can compensate the nonlinear zoom ring pretty much directly.

In order to turn the varifocal lens into a parfocal one, you'd have to automatically adjust the focus depending on the current focal length (and the relationship between them obtained during calibration).

If you did the inverse (adjusting focal length according to focus), that would prevent any focus breathing the lens might have.

In conclusion:

1. With the ability to rotate and measure the position of both zoom and focus ring on a lens automatically, the hardware becomes general purpose and applicable to (pretty much) any lens.
2. Both requirements (parfocal lens, linear zoom throw) are abstracted away from the lens itself and are now a job of your software that controls the two rings, which allows you to use lenses that are neither parfocal nor have a linear zoom throw and thus cheap.
3. Given that the lenses deviate from the original requirements in a static manner, they can be calibrated. That means that the software that controls the automated rings of the lens is also universal and all that needs to change in order to use a different lens is to use a different calibration.

By making parfocality1 of the lens and linearity of its zoom a property of the system surrounding the lens, the lens does not have to have these properties any more, which enables you to use plenty of other (cheaper) lenses.

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1 that's totally a word