On Wed, Jul 29, 2020 at 07:36 AM, <jsalbinson@...> wrote:

Still digesting some of the earlier comments, but the tan(theta)/theta function worries me a bit as both tan(theta) and theta go to zero, while the ratio analytically goes to 1, I doubt the computer can cope with zero/zero - it usually falls over. Therefore I found a series expansion for tan(theta), divided it by theta to get a series = 1+ term in theta**2 + term in theta**4 + term in theta**6. USe of a decent spread sheet, but putting in the zero terms by hand, give the result I commented on earlier. I will have another look at the code to see what I am missing. More coffee...

Below is how I see it, at least for a TA drive with a "sliding pivoting arm" i.e. the screw is fixed relative to the axis and the arm travels along it. I'm no expert on TA's but I also didn't find much design info. online so this is my best understanding. I kept things simple by using unity for the radius and 100 tpi for the screw.

1. As shown with the arm perpendicular to the screw the ratio is exactly 628:1.

2. To reach a real axis angle of 45° you would need 1" of travel. Since tan(45) = 1 this checks out (1 * 100 = 100 steps if working at 1 step per rotation of the screw.) The axis angle of 45 degrees = 0.785" of circumference.

3. To reach a real axis angle of 63.4° you would need 2" of travel. Since tan(63.4) = 2 this checks out (2 * 100 = 200 steps if working at 1 step per rotation of the screw.)

4. If the TA is at 150 steps and you want to know the axis angle atan(150/100) = 56.30° which in angular steps (as opposed to angular degrees) would be 56.30 * (628/360) = 98.21 steps.