So just what was a "warped board"?

[raj]

Hello everybody!

I am currently drawing designs of wheels that would maintain weights symmetry through rotation, and this reminded of bessler clue ' warp board' I read sometime back on this forum.

While searching this forum, I came upon this thread and the discussion whether the translation meaning should be 'warp' or 'elongated'.

I just remembered from school days maths, that the shortest distance between two points is a straight line.

Therefore the only way, we could elongate the path between two points in a wheel is to curve, twist, or zigzag the path, i.e warp it, so to say.

Raj

[johannesbender]

the circle already includes this particular feature .

long ago ,I was playing around with all kinds of geometry features I could come up with from circles , when I realised something I didn't really pay attention to before that time .

the arc length of a circle from 0 to 180 degrees is obviously longer than the length of its diameter.

so you can calculate that it takes half the circumference of a circle to lift something in the centre from bottom to top along the diameter , higher / along a longer distance , than the arc length of half the circumference .

so it could theoreticly take only 180 degrees of rotation to lift something higher than the fall height , however not as magical as it sound at first when I thought about it..

jb

[Stewart]

Hi Raj

Neither 'warped' nor 'elongated' is a correct translation.

Here's my transcription of that section of the Latin text in the original letter (the words between the ~ characters were crossed out):
"... In peripheria enim hinc inde affixae erant trabeculae normales, ad quas in circumactione rotae allidi pondera ~manifestum erat~ satis clare percipiebatur. Trabeculas illas per rimam intuens adverti, quamvis e longinquo. ..."

And my translation:
"... In fact in the periphery [of the wheel] here and there small 'normal' beams were attached, which on rotation of the wheel ~it was evident~ were quite clearly perceived to be hit by weights. I have noticed those small beams [while] looking through a crack, although from a distance. ..."

I think the original confusing translation of 'warped boards' must be related to the words 'trabeculae normales'. I still can't see how someone would arrive at a translation of 'warped' though. 'Trabeculae' is diminutive plural of 'trabs' which means a beam or plank etc., so we get small beams/planks. 'normales' is an adjective (normalis/normale) which means "right angled, made according to a carpenter's square". The word 'normal' in English wasn't used to mean "conforming to common standards, usual" until the early 1800s. So when talking about 'normal' beams/lines in a wheel/circle I would think this would mean beams/lines at right-angles to the tangent.

Another thing to point out is that 'hinc inde' generally means 'here and there', but could mean in this case 'on both sides'. (hinc inde = 'here and there', 'from different directions', 'on both sides', 'on the one hand and on the other')

The incorrect translation of 'elongated' comes from the end of the sentence where "e longinquo" has been mistaken for one word instead of the 'e' being a separate word. It has nothing to do with a description of the boards/beams and means "from a distance".

For something that seems to fit Wolff's description quite closely, have a look at MT18. It has weights attached to elastic arms and 'normal' beams/planks on the periphery of the wheel that the weights hit and rest on.

Here's another topic where this subject was discussed in detail:
http://www.besslerwheel.com/forum/viewtopic.php?t=2539

Stewart