geometry question (the irritation of forgetting stuff!)

[Screwdriver]

Nothing shown so far as I can tell. One assumes the constraint is provided by the operator and some unseen other features.

 

[hotponyshoes]

You'll need to provide the location of at least one pivot point.

If it's not important, I'll pick a pivot point for you..
On the fixed block put the pivot 40 in from the right hand side (centered vertically)
To stick with a vertically centered pivot on the moving block put that one 95.51 from the right hand side and you'll be there.
Orange (link bar) will be 160.81 between centers.

 

[voipio]

As I see it, the points where the arms are attached to the two "modules" are shown in the right place in the original posting. Anything else won't keep the intended positions when open and shut. But, both ends of the "orange line" arms will need to pivot, plus there will be an additional need for a joining rod between the arms at each end of the modules, to stop it all getting too floppy.

There is another solution, which would provide greater mechanical constraint, and involve basically a hinge, where the pivot point would be at half the height of the gap between the modules in the closed position, and set approximately 10.04mm (actually slightly less than 10.04mm, because of the 11 degree angle) behind the rear of the modules in the closed position.

 

[julianf]

You'll need to provide the location of at least one pivot point.

If it's not important, I'll pick a pivot point for you..
On the fixed block put the pivot 40 in from the right hand side (centered vertically)
To stick with a vertically centered pivot on the moving block put that one 95.51 from the right hand side and you'll be there.
Orange (link bar) will be 160.81 between centers.

That, pretty much, works! I think my minor error is somthing to do with multiple re-draws in CAD, but, its basically working.

Can you show me the sum you used in more detail, so as i can move around the pivot point on block #1 to suit the design better? Its not a fixed requirement, but, with your working, i can load up a spread sheet with the numbers, and see what it spits out for block #2 when i move block #1's point.

Ive been trying to do this for ages now, and, whilst your numbers work, im still unsure how to calculate them for myself!

Thank you.

 

[julianf]

As I see it, the points where the arms are attached to the two "modules" are shown in the right place in the original posting. Anything else won't keep the intended positions when open and shut. But, both ends of the "orange line" arms will need to pivot, plus there will be an additional need for a joining rod between the arms at each end of the modules, to stop it all getting too floppy.

There is another solution, which would provide greater mechanical constraint, and involve basically a hinge, where the pivot point would be at half the height of the gap between the modules in the closed position, and set approximately 10.04mm (actually slightly less than 10.04mm, because of the 11 degree angle) behind the rear of the modules in the closed position.

Theres other stuff going on to stop it flopping about. I actually built the thing before (no easy photos now) but it was years ago and i just cant remember how the points were calculated. Im sure i did it in CAD with intersecting arcs, but @hotponyshoes seems to have done it with an equation.

 

[hotponyshoes]

That, pretty much, works! I think my minor error is somthing to do with multiple re-draws in CAD, but, its basically working.

Can you show me the sum you used in more detail, so as i can move around the pivot point on block #1 to suit the design better? Its not a fixed requirement, but, with your working, i can load up a spread sheet with the numbers, and see what it spits out for block #2 when i move block #1's point.

Ive been trying to do this for ages now, and, whilst your numbers work, im still unsure how to calculate them for myself!

Thank you.

Not without a given pivot point.
With the 2nd block in the top position the left hand edge is at 0⁰.
In the lower position they are at 79⁰ so that gives you 2 angles. From that you only need one dimension to work out all the other sizes on a triangle, hence why I've used 40 as a start point.
I suppose you could put a formula into a spreadsheet to show you the position of the pivot on one block in relation to the other but you'll still have to define one first even if it's just centering vertically or something

 

[julianf]

Not without a given pivot point.
With the 2nd block in the top position the left hand edge is at 0⁰.
In the lower position they are at 79⁰ so that gives you 2 angles. From that you only need one dimension to work out all the other sizes on a triangle, hence why I've used 40 as a start point.
I suppose you could put a formula into a spreadsheet to show you the position of the pivot on one block in relation to the other but you'll still have to define one first even if it's just centering vertically or something

Yep, thats what i mean -

I could put it into a sheet, and enter my preference for block #1 pivot, and then see if the position it spat out for block #2 pivot were favorable to me.

What youve given me works, which is what i was struggling so much with, but there may be more optimal layouts.

 

[julianf]

tankards of ale (tangent over adjacent?)
cigarettes are horrible (something something hypotenuse?)

...and i cant remember the third one

its been a long time since gcse maths!

 

[tom2207]

ten old angels ...................................... tan op over adj
singing over heaven ........................................ sine opp over hyp
carrying a harp .......................................... cos adj over hyp

 

[hotponyshoes]

Yep, thats what i mean -

I could put it into a sheet, and enter my preference for block #1 pivot, and then see if the position it spat out for block #2 pivot were favorable to me.

What youve given me works, which is what i was struggling so much with, but there may be more optimal layouts.

That would be doable.
It's going to be quite a long list of possible positions if you are working to 2 decimal places though.

How are you defining the criteria for the 'optimal layout'
You'll want a filter to search the results for that..

 

[julianf]

The hinge / tie bar also operates as a stop to maintain the angle of the #2 block.

So it has other functions, some cosmetic, some mechanical, but they are all way more flexible, and I can just prototype them "by eye", so long as I use your method of making sure the options work with the folding.

What I mean is, I don't need mathematical constraints on the rest of it. I can just sort it out by eye, using the data spat out by your solution.

 

[hotponyshoes]

The hinge / tie bar also operates as a stop to maintain the angle of the #2 block.

So it has other functions, some cosmetic, some mechanical, but they are all way more flexible, and I can just prototype them "by eye", so long as I use your method of making sure the options work with the folding.

What I mean is, I don't need mathematical constraints on the rest of it. I can just sort it out by eye, using the data spat out by your solution.

I'll have another think about that tonight.
The problem with my solution is it needs more constraint on the input.
That's why I had to add the 40×center position of the fixed pivot as there is not enough information to make a triangle otherwise.

Other fixed points would work.
Ie, if you had a desired angle you wanted the orange bar to sit at one end or the other.
You need at least 3 numbers to work out the size of a triangle. The angles or the length of the sides. You need at least one of each.

 

[Stueeee]

ten old angels ...................................... tan op over adj
singing over heaven ........................................ sine opp over hyp
carrying a harp .......................................... cos adj over hyp

The mnemonic we were taught:

Some Opera Houses.....................Sine
Can Always Have .........................Cosine
Their Overtures Again...................Tangent

 

[Screwdriver]

i just cant remember how the points were calculated. Im sure i did it in CAD with intersecting arcs, but @hotponyshoes seems to have done it with an equation.

Do you want to do it by construction as shown here:

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....

Or do you want a calculation? Clearly the triangle is formed by the green, orange and blue at one point in the movement since their lengths must be fixed in order for the starting and finish positions to be physically possible. That triangle only appears once during the sweep of the mechanism due to the offset X and the irregular start position. The second potential solution where the white circels intersect is not physically realised due to the intersection of the blocks.

In case I did not explain. The left hand green arrow is a construction, you determine its length from the diagram. Then move that arrow to the intersection of the two orange radii (the white circles).

If you require an offset of X, then the distance from the above intersection will tell you X for any given green/orange.

The complication in a calculation is the relationship of the start/finish angle which you would need to specify if you wanted to triangulate a solution

 

[julianf]

I dont mind how i do it, but, in truth, whilst @hotponyshoes ' method more or less works, i dont understand either option.

​

This ^ is my data, from this image -

Basically, what id like to do is place the pivot on block #1, and generate the co-ordinates for block #2 - spreadsheets, curves, whatever, i dont care!

...but i do need to understand the method, otherwise im stuck at one answer, and can not make adjustments.

 

[hotponyshoes]

I did have another got at this last night.
But, it's hot, I was tired, and my laptop is struggling with the big numbers.

The first problem is this,
Say the diameter of the pivot is 10 and you want to allow a safety margin around the edges of the block of 5.
And saying you want to work to 2 decimal places.

That gives you 121738900 possible positions for the pivot on block 1.

Define your whole previous drawing (including both positions of block 2) with an x&y axis. Make 0:0 the bottom left corner of the fixed block.

Put a formula into the spreadsheet to populate column 1 with all the possible positions.
Ie, cell 1 #name1(x=0.00,y=00) cell 2 #name+1(=#1 x+0.01, y=0.01)
That's as far as i got as it wasn't finished doing that when I left for work this morning!

Next, define the minimum and maximum arc length of the orange rod (take these from the drawing) which (if you include the pivot/margin should be 76 & 390.51 so you can restrict the calculations to a range of 31451 positions.

The next step needs some thinking about as it's going to need some serious computing power (or time)

The easy way would be to calculate the coordinates of each point of a 36000 segment circle, for each possible arc length at each possible starting point.

Then remove all lines where any columns contain a negative number.

Then, all you need to do is create a formula to populate 2 other columns for block 2 in borh positions offsetting the usable coordinates against block 1 (ie, give them both new coordinates starting 0:0 at the bottom left of both blocks.
(Not sure how you do that for the one at 11⁰?)

Then just a formula to search the 2 columns for the 2 positions of block 2 for coordinates that match on both blocks.
Those will be all possible working positions.

Populate those into another list,
You'll then need to run thorough that list again with an offset against the bottom corner of block 2 in the top position removing all entries that don't match with the 56 gap coordinate.
Then the top corner of block 2 in the bottom position that don't match with the gap required there.

The less intensive way (for the computer) would be to define the 2 coordinates for the possible mount points on block 2 in both positions and then only generate arcs within those points.

I think, at the least, you'll need to drop to 0 decimal places just to get the average PC to cope..