Multiple Rotating Signs on a Fence Gate -- Overlap Question

[scatterbrainz]

TL;DR Summary

Math - Trig or Physics - Vectors

Hey Everyone,

This is a little project of mine. I'm including a daigram of it - top view -> down. This is part of a larger system.

Consider a fence gate made of poles. In my diagram Point "A" in blue is a non-moving vertical pole. Point "B" red is a pivot point for an arm containing all the points of "C" - purple. Each brown block represents a wood sign that is 5.5 inches wide. Sign "A" rotates around axis "A", signs "B", "C", "D", rotates around their respective axis "C".

The question is, when the arm rotates on axis "B", to a 42.5 deg (+/- 2.5 deg)angle, is the spacing sufficient so that the signs do not overlap each other?

For consideration: when the arm is along the x-plane - the spacing between signs is roughly 5.5 inches, however, it appears to be only 1.5 inches when it is rotated out to 42.5 deg (+/- 2.5 deg). If I remember back to my physic days this screams displacement, but its not just about where the point is when it rotates, its visual space between signs also. Ideas? thoughts ?

 

[pbuk]

thoughts ?

Your measurements for the sign on the fixed post and the pivot are inconsistent - if the distance to the pivot is 13.5" the first sign will be further than 5.5" from the next when the pole is "horizontal" as in your drawing. Also this arrangement will not lead to a consistent spacing between all signs as the gate is rotated due to the offset between A and B.

Also 5.5" is more than 127 mm so I am going to ignore the metric measurements.

The diagram is well drawn and must have taken some time: it is important to take as much time and care with accuracy of measurements. Perhaps you could use CAD software - there are free tools available.

Anyway, assuming the signs are actually 5.5" wide and are at centres 11" apart:

• From the diagram you should be able to see that the limiting case is formed by a right angled triangle with hypotenuse 11" (the distance between the centre of the signs) and shorter side 5.5" (the width of the signs).
• The limiting angle is therefore $\sin^{-1} \frac {5.5}{11} = 30°$.
• At 42.5° the distance between centres is $11" \sin 42.5° \approx 7.43"$ which gives a gap between the signs of about 1.9".

 

[scatterbrainz]

Your measurements for the sign on the fixed post and the pivot are inconsistent - if the distance to the pivot is 13.5" the first sign will be further than 5.5" from the next when the pole is "horizontal" as in your drawing. Also this arrangement will not lead to a consistent spacing between all signs as the gate is rotated due to the offset between A and B.

Also 5.5" is more than 127 mm so I am going to ignore the metric measurements.

you are correct - when I converted via google - I probably forgot to hit enter - as 5.5 = 139.7mm 5.0 = 127 mm. Thank you for catching that

The diagram is well drawn and must have taken some time: it is important to take as much time and care with accuracy of measurements. Perhaps you could use CAD software - there are free tools available.

Anyway, assuming the signs are actually 5.5" wide and are at centres 11" apart:

• From the diagram you should be able to see that the limiting case is formed by a right angled triangle with hypotenuse 11" (the distance between the centre of the signs) and shorter side 5.5" (the width of the signs).
• The limiting angle is therefore $\sin^{-1} \frac {5.5}{11} = 30°$.
• At 42.5° the distance between centres is $11" \sin 42.5° \approx 7.43"$ which gives a gap between the signs of about 1.9".

 

[scatterbrainz]

Thanks for the answer. I just need to make sure the signs are visible on an angle. I've updated the drawing to show 3 stages, and adjusted what I think to be the measurements. Hopefully I haven't made any careless conversion mistakes. Let me know your thoughts ?

 

[Lnewqban]

Thanks for the answer. I just need to make sure the signs are visible on an angle. I've updated the drawing to show 3 stages, and adjusted what I think to be the measurements. Hopefully I haven't made any careless conversion mistakes. Let me know your thoughts ?

Sorry, this last posted drawing shows up too blurry to see any fonts.

If you don't mind, I have a few questions:
1) What is the meaning of that Base unit?

2) Which stage is full opened and full closed?

3) What is the direction of the line of sight for which to avoid overlapping (I assume some gap is acceptable)?

4) What makes each sign suddenly rotate 90° between stages 1 and 2?

5) Why is a new stage 3 shown in the second diagram if you have initially specified the gate to open (or close) to a precise 42.5°+/- 2.5° angle?

6) What measurement units are you going to be working with during construction?