geometry question (the irritation of forgetting stuff!)

[julianf]

So, this is a hinged "thing"

Block #1 is fixed. Block #2 (shown in two positions in the diagram, but is only actually one part) moves. Maybe call the two positions flat (even though its not flat) and folded.

Distance x (in the folded position) is fixed.


The orange line is a fixed bar of fixed distance.

The pivot points can be moved.


My problem -

(and ive done this before, but not for a few years, and its so frustrating that i cant remember how!)

The pivot point on block #2 - i cant work out where its supposed to go!

Obviously it has to be in the same position on block #2 in the flat and folded positions. The diameter of the white circle (the length of the orange bar) can change.

The config shown is close to working, as i, mostly, coppied it from a working one that i did years ago, but i need to change some of the distances, and i just cant work out how to position anything now!


I recall its done with arcs, and where those arcs intersect, but i keep staring at it, and its hurting my brain!

The only thing i really care about is distance x, and the angle between 1 and 2 when "flat" (not flat - #2 is actually tilted by 11 degrees)

Have i explained myself even half sensibly?

Again, i did it before just using lines - there was no messing about, but i just cant remmeber how now!

 

[sako243]

You basically need to create some simultaneous equations that define the length (say it's called h) of the orange bar when it's in both positions. Set them equal to each other and start solving.

As it stands your problem is too undefined (I think) for it to be solved emperically. E.g. Are the pivot points in the same location in the blocks? If not then unless you start constraining things you won't be able to get any numbers.

 

[Barking Mat]

Roughly 90°, yes, I'll have another beer if you insist.

 

[julianf]

You basically need to create some simultaneous equations that define the length (say it's called h) of the orange bar when it's in both positions. Set them equal to each other and start solving.

As it stands your problem is too undefined (I think) for it to be solved emperically. E.g. Are the pivot points in the same location in the blocks? If not then unless you start constraining things you won't be able to get any numbers.

I think that, when I did it before, the pivot points were fixed (the holes pre made) but I'm not certain.

But even choosing a fixed point on #1, distance x defined, and considering the only variables to be the points on block #2, I'm still struggling.

 

[julianf]

Pivot points can be anywhere on both blocks (but can not move on block 2 when opening and closing - ie it's a fixed point, not a slider)

But even if I just choose a point on #1, I still can't work out #2.

My irritation is that I've done it before, but maybe I had a fixed point on both blocks then, and varied the distance between them in the "flat" position to accommodate my fixed (x) dimension.

 

[More Amps]

If you get really stuck, there's always good old "trial and error". Grab a few bits of scrap timber and start experimenting - it shouldn't take too long to narrow down the options...

 

[tom2207]

start from the finished point in the diagram , is the start point vital or will anything that opens do ,,, if its the latter , make a cardboard one and mess about with it ,

 

[Agroshield]

Where block 2 is directly above block 1, the vertical edges of each coincide.

That fact, if it is a fact and not just artistic license, and distance X, is enough fully to define the problem.

As above, a cardboard model will work very well for solving this.

 

[hotponyshoes]

What exactly are you trying to work out?

If you want to stop the blocks hitting each other then you'll need to use arcs(or just make the orange bar longer )

If you just want to position them correctly to X then it's just X plus the Z dimension of one block (if you put the pivots in the center)

If you want it to be self-holding in the top position (ie, gone past 90⁰) the you'll want to use triangles for X then arcs to check clearance.

I'd start by working out the minimum arc length for clearance then add to that to get the self-holding length.

You'll need to provide the dimensions of X and the dimensions of the visible side of the blocks. Or you could use a formula with X and Y/Z but you'll also want to provide A for the holding angle

 

[Kram]

Does the circle on the centreline of (2) pivot on the small circle in (1), in which case the orange bar will always have the same length but the distance between the blocks, X will change depending on their position and rotation.

Anything else and you need to redraw it properly to get a sensible answer, IMO.

 

[julianf]

What exactly are you trying to work out?

where the pivot points should be on each block, to maintain the positions of the blocks shown in both the flat and folded positions

so -

the position of the pivot on block 1
the position of the pivot on block 2

 

[hotponyshoes]

where the pivot points should be on each block, to maintain the positions of the blocks shown in both the flat and folded positions

so -

the position of the pivot on block 1
the position of the pivot on block 2

If those are the only requirements then all you need to do is X+C+D+(S×2)

X= gap in drawing
C= clearance required between blocks
D = diameter of pivot pin
S = safety factor (distance between outside of pivot pins and the edge of the block)

 

[addjunkie]

If all else fails scale drawings…

 

[julianf]

If those are the only requirements then all you need to do is X+C+D+(S×2)

X= gap in drawing
C= clearance required between blocks
D = diameter of pivot pin
S = safety factor (distance between outside of pivot pins and the edge of the block)

I cant pretend i understand your sum, but i think the above measurements show everything?

Id be right pleased if you could show me how it should be worked out!

Thank you.

 

[julianf]

I cant see how D (diameter of the pivot pin) is relevant to its placement, but then i dont understand your equation, so anyhing is fine with me - 10mm, whatever.... I cant see that its diameter will change its position, as im talking about a center from which to pivot?

 

[julianf]

to remove confusion -

blue (on the left) highlights the flat positon
yellow (on the right) highlights the folded postion

blue is not actually flat, as the second unit ends its travel at an 11 degree tilt

 

[julianf]

If all else fails scale drawings…

all the screen grabs are to scale, with the dimensions now added

 

[Pigeon_Droppings2]

I could do the maths but it would mean starting up my brain and I think it would hurt so I'll wait and hopefully someone else will solve it.

 

[Screwdriver]

If you want to construct a solution using a compass, I'm pretty sure this is correct (don't shoot me!)

The two white circles (orange radius) represent every possible position of the target corner in both positions.

The green arrow is the length the target corner must be from block 1 pivot when it meets X.

Where the two white circles meet tells you where the target corner must be X distance from the green vector. You know the length of the green vector, draw it in place and you could even draw a blue circle to show the X distance but that overcomplicates things....

The key issue I think is that block 2 needs to be oriented as shown when target corner reaches X and you can find that solution by intersecting the white circles as above.

Personally, I'd just knock it out in Sketchup or some inferior design package where I'd be drawing intersecting circles until my eyes bleed....

 

[tom2207]

but whats going to ensure the order the two pivots swing in ,,,, you may just end up with something totally different as theres no constraints on either pivot point , and if its a pair of hinges they will move independent of each other no matter how pretty the picture ,,,, just saying.