̽��ֱ�� of Cambridge - friction

Study reveals Leonardo da Vinci’s “irrelevant” scribbles mark the spot where he first recorded the laws of friction

tdk25 — Thu, 21 Jul 2016 14:19:45 +0000

Scribbled notes and sketches on a page in a notebook by Leonardo da Vinci, previously dismissed as irrelevant by an art historian, have been identified as the place where he first recorded his understanding of the laws of friction.

̽��ֱ��research by Professor Ian Hutchings, Professor of Manufacturing Engineering at the ̽��ֱ�� of Cambridge and a Fellow of St John’s College, is the first detailed chronological study of Leonardo’s work on friction, and has also shown how he continued to apply his knowledge of the subject to wider work on machines over the next two decades.

It is widely known that Leonardo conducted the first systematic study of friction, which underpins the modern science of “tribology”, but exactly when and how he developed these ideas has been uncertain until now.

Professor Hutchings has discovered that Leonardo’s first statement of the laws of friction is in a tiny notebook measuring just 92 mm x 63 mm. ̽��ֱ��book, which dates from 1493 and is now held in the Victoria and Albert Museum in London, contains a statement scribbled quickly in Leonardo’s characteristic “mirror writing” from right to left.

Ironically the page had already attracted interest because it also carries a sketch of an old woman in black pencil with a line below reading “cosa bella mortal passa e non dura”, which can be translated as “mortal beauty passes and does not last”. Amid debate surrounding the significance of the quote and speculation that the sketch could represent an aged Helen of Troy, the Director of the V & A in the 1920s referred to the jottings below as “irrelevant notes and diagrams in red chalk”.

Professor Hutchings’s study has, however, revealed that the script and diagrams in red are of great interest to the history of tribology, marking a pivotal moment in Leonardo’s work on the subject.

̽��ֱ��rough geometrical figures underneath Leonardo’s red notes show rows of blocks being pulled by a weight hanging over a pulley – in exactly the same kind of experiment students might do today to demonstrate the laws of friction.

Professor Hutchings said: “ ̽��ֱ��sketches and text show Leonardo understood the fundamentals of friction in 1493. He knew that the force of friction acting between two sliding surfaces is proportional to the load pressing the surfaces together and that friction is independent of the apparent area of contact between the two surfaces. These are the ‘laws of friction’ that we nowadays usually credit to a French scientist, Guillaume Amontons, working two hundred years later.”

“Leonardo’s 20-year study of friction, which incorporated his empirical understanding into models for several mechanical systems, confirms his position as a remarkable and inspirational pioneer of tribology.”

Professor Hutchings’s research traces a clear path of development in Leonardo’s studies of friction and demonstrates that he realised that friction, while sometimes useful and even essential, also played a key role in limiting the efficiency of machines.

Sketches of machine elements and mechanisms are pervasive in Leonardo’s notebooks and he used his remarkably sophisticated understanding of friction to analyse the behaviour of wheels and axles, screw threads and pulleys, all important components of the complicated machines he sketched.

He wanted to understand the rules that governed the operation of these machines and knew that friction was important in limiting their efficiency and precision, grasping, for example, that resistance to the rotation of a wheel arose from friction at the axle bearing and calculating its effect.

“Leonardo’s sketches and notes were undoubtedly based on experiments, probably with lubricated contacts,” added Hutchings. “He appreciated that friction depends on the nature of surfaces and the state of lubrication and his use and understanding of the ratios between frictional force and weight was much more nuanced than many have suggested.”

Although he undoubtedly discovered the laws of friction, Leonardo’s work had no influence on the development of the subject over the following centuries and it was certainly unknown to Amontons.

“Leonardo da Vinci’s studies of friction” by Professor Ian Hutchings is published in the journal Wear. ̽��ֱ��paper can be accessed in full via: https://www.sciencedirect.com/science/article/pii/S0043164816300588

or https://www.ifm.eng.cam.ac.uk/uploads/Hutchings_Leonardo_Friction_2016_v2.pdf

A general article on tribology that discusses its importance in modern engineering can be found at:

https://www.ingenia.org.uk/Content/ingenia/issues/issue66/hutchings.pdf

A new detailed study of notes and sketches by Leonardo da Vinci has identified a page of scribbles in a tiny notebook as the place where Leonardo first recorded the laws of friction. ̽��ֱ��research also shows that he went on to apply this knowledge repeatedly to mechanical problems for more than 20 years.

̽��ֱ��sketches and text show Leonardo understood the fundamentals of friction in 1493

Ian Hutchings

V&A Museum, London

Codex Forster III folio 72r

̽��ֱ��text in this work is licensed under a Creative Commons Attribution 4.0 International License. For image use please see separate credits above.

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How stick insects honed friction to grip without sticking

fpjl2 — Wed, 19 Feb 2014 12:38:20 +0000

When they’re not hanging upside down, stick insects don’t need to stick. In fact, when moving upright, sticking would be a hindrance: so much extra effort required to ‘unstick’ again with every step.

Latest research from Cambridge’s Department of Zoology shows that stick insects have specialised pads on their legs designed to produce large amounts of friction with very little pressure. When upright, stick insects aren’t sticking at all, but harnessing powerful friction to ensure they grip firmly without the need to unglue themselves from the ground when they move.

In a previous study last year, the team discovered that stick insects have two distinct types of ‘attachment footpads’ - the adhesive ‘toe pads’ at the end of the legs, which are sticky, and the ‘heel pads’, which are not sticky at all. ̽��ֱ��insect uses different pads depending on direction and terrain.

By studying the ‘heel pads’ in more detail, researchers discovered the insects have developed a way to generate massive friction when walking upright. They do this through a system of tiny hairs that use combinations of height and curvature to create a ‘hierarchy’ of grip, with the slightest pressure generating very strong friction - allowing stick insects to grip but not stick.

̽��ֱ��researchers say the study - published today in the Journal of the Royal Society Interface - reveals yet another example of natural engineering successfully combining “desirable but seemingly contradictory properties of man-made materials” - namely, the best of both hard and soft materials - simply through clever structural design.

“Just by arrangement and morphology, nature teaches us that good design means we can combine the properties of hard and soft materials, making elemental forces like friction go a very long way with just a small amount of pressure,” said David Labonte, lead researcher from the Department of Zoology.

̽��ֱ��power of friction relies on ‘contact area’, the amount of close contact between surfaces. In rigid materials, such as steel, even the tiniest amount of surface roughness means there is actually relatively little ‘contact area’ when pressed against other surfaces - so any amount of friction is very small.

On the other hand, soft materials achieve a lot of contact with surfaces, but - due to the larger amount of contact area - there is also a certain amount of adhesion or ‘stick’ not there with hard materials.

To solve this, stick insect’s hairy friction pads employ three main tricks to allow contact area to increase quickly under pressure, creating a scale or ‘hierarchy’ of grip with absolutely no stick:

• Both the pad itself and the tips of the hairs are rounded. This means that, when pressure is applied, more contact area is generated - like pushing down on a rubber ball.
• Some hairs are shorter than others, so the more pressure, the more hairs come into contact with the surface.
• When even more pressure is applied, some of the hairs bend over and make side contact - greatly increasing contact area with very little extra force.

These design features work in harmony to generate large amounts of friction with comparatively tiny amounts of pressure from the insect. Importantly, there is hardly any contact area without some tiny amount of pressure - which means that the specialised ‘frictional hairs’ don't stick.

Arrays of tiny hairs have been found before, for example on the feet of geckos, beetles and flies. However, these hairs are designed to stick, and are used when creatures are vertical or hanging upside down.

Sticky hairs are completely aligned and have flat tips - meaning that they immediately make full contact that hardly changes with additional weight - as opposed to friction hairs, with their higgledy-piggledy height ranges and rounded tips.

“We investigate these insects to try and understand biological systems, but lessons from nature such as this might also be useful for inspiring new approaches in man-made devices,” said Labonte.

He uses the example of a running shoe as a possible man-made item that could be enhanced by stick insect engineering: “If you run, you don’t want your feet to stick to the ground, but you also want to make sure you don’t slip.”

Adds Labonte: “Stickiness is the force that is needed to overcome when trying to detach one thing from another. If the soles of your feet were made of Scotch tape, it may be helpful when you are walking up walls or hanging upside down, but the rest of the time it would be incredibly frustrating.”

“Stick insects have developed an ingenious way of overcoming the conflict between attachment and locomotion, with a dual pad system that alternates between stick and grip depending on the situation.”

Inset image: Scanning electron microscopy image of conical, micrometre-sized outgrowths that cover the tarsal ‘heel pads’ of some stick insects (false colours). Image by David Labonte & Adam Robinson.

Scientists have discovered that, when upright, stick insects don’t stick. Instead, they deploy special hairy pads designed to create huge amounts of friction from the tiniest of pressure increases - ensuring that the insects grip but don’t stick.

Lessons from nature such as this might also be useful for inspiring new approaches in man-made devices

David Labonte

Thomas Endlein

Stick insect

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