Nobody replying, so I’ve reframed the question
A 24V DC motor has an optical encoder with 500 divisions which outputs the pulse frequency to an electronic counter/timer. The motor has a flat pulley of 31.827mm diameter used as a tape drive.
(a) Calculate the resolution in linear travel of...
Solution?
OK, I think I have it. This is entirely thanks to Astronuc getting me to treat this as successive levers:
http://www.geocities.com/zakcapriturbo/bourdon_diag04.jpg
And:
http://www.geocities.com/zakcapriturbo/bourdon_formulas01.jpg
Anybody agree?
Even more thoughts
Looking at the above again, I see that it is wrong since it doesn't include the length of the pointer (which we can call R4).
But I think I'm on the right track here but both radius R4 and angle X3 are unknown, so...more work needed !
More thoughts
From what you said, I realize now that this diagram is a better representation of what I have. It certainly makes things easier for me to understand:
http://www.geocities.com/zakcapriturbo/bourdon_diag03.jpg
So, I've omitted that X3 is an angle and just called it linear...
Hi Astronuc,
Grateful for your reply.
Could you explain that a bit more? I don't quite understand your notation.
What do you mean by "the https://www.physicsforums.com/latex_images/12/1201015-0.png of the surfaces" ?
And https://www.physicsforums.com/latex_images/12/1201015-1.png...
Homework Statement
http://www.geocities.com/zakcapriturbo/bourdon_diag02.jpg
A pointer is connected to an arm that moves along a single axis via a pinion gear wheel and gear quadrant. A displacement of the arm (x) results in an angular movement of the pointer (X3).
Knowns...
Solution
I have decided to use approximation. I converted the frustum to a whole cone to make the approximation leg-work easier. It isn't what you'd call satisfactory but it works.
1: You know the volume of the frustum (V1) so the volume of half-filled frustum is half that value (V2).
2...
I'm thoroughly beaten
The equations I derived in the last post are slightly wrong. They should be:
http://www.geocities.com/zakcapriturbo/Q4_physicsforum_equations05.jpg
I am now fundamentally stuck at this point. For clarity, I have represented the the above expression thus:
a = h2
b...
More progress
Hi again,
Been doing a bit more work. I decided that I preferred working with radius values and the side wall angle (rather than diameter and inclusive angle):
http://www.geocities.com/zakcapriturbo/Q4_physicsforum_equations03.JPG
This means that:
Volume = pi/3 x h x...
More progress
Thanks integral. I feel like I am getting somewhere although there is a way to go yet.
I have arranged everything so that the equations better represent the specific problem I am trying to solve:
Equation for partially-filled volume...
Thanks again.
It's not pretty but I've found that if I rearrange so that d2 is the subject, it still leaves h2 on the other side.
Basically:
http://www.geocities.com/zakcapriturbo/tan_02.JPG
I've been looking and I can now see that your expression is for the total inclusive angle of the side walls with the top of the cone (i.e. 90 degrees minus the angle with the base of the cone, as in my expression above).
I had sat and worked through the idea of using the 90 degree triangle...