Objectives_template
Module 5 : Basic Paradigms
Lecture 11 : Torus, Coil, Helicoids, Spiral
The Lecture Contains:
Torus
Coil
Helicoids
Spiral
file:///E|/Ayush%20NPTEL%20Course/DESIGN_PARADIGM/lecture11/11_1.htm [2/19/2013 11:09:28 AM]
Objectives_template
Module 5 : Basic Paradigms
Lecture 11 : Torus, Coil, Helicoids, Spiral
(Read more: http://en.wikipedia.org/wiki/File:Fibonacci_spiral.svg ; Aug 4, 2012)
A spiral continually changes in radius (plate 16B). The change might be linear, increasing at a constant
rate, or the rate of change itself might increase at a steady rate, in which case we call it logarithmic
spiral. A linear increasing radius can be demonstrated by winding a rope into a spiral. A logarithmic
spiral can be seen on the underside of most snail shells (plate 17A).
Plate 17A Spiral Snails
17B Centipede
17B CD Track
(Source : http://www.google.co.in/search?hl=en&q=Spiral+snails&bav=on.2,or.r_gc.r_pw.r_qf
.&biw=1328&bih=574&um=1&ie=UTF-8&tbm=isch&source=og&sa=N&tab=wi&ei=1cAcUPucB
ofOrQeS-YD4AQ ; Aug 4, 2012
Plate17A&B : http://www.google.co.in/search?hl=en&q=Spiral+in+nature&bav=on.2,or.r_g
c.r_pw.r_qf.&biw=1328&bih=574&um=1&ie=UTF8&tbm=isch&source=og&sa=N&tab=wi&ei=
6DkdUJO3Dc3orQf3n4CgDg#um=1&hl=en&biw=1328&bih=574&tbm=isch&sa=X&ei=yDodU
OLiJcvNrQeKqoDgAQ&ved=0CEMQvwUoAQ&q=Spiral+in+centipede&spell=1&bav=on.2,or
.r_gc.r_pw.r_qf.&fp=dd0db88348be4c18 ; Aug 4, 2012)
Human beings have applied the mechanism of spiral quite efficiently for various purposes. The spiral
formation among insects is very effective defence mechanism that makes a compact body (plate 17B)
and protects from possible prey. Snails under threat from the prey contract their body inside the hard
spiral-shell so that prey cannot reach easily inside. By forming spiral formation centipede create a much
stronger compact body-structure from any outside threat (plate 17B). A spiral is a good way to compact
something that would otherwise be long. Thus, as mentioned in the disc paradigm, something like a
music CD (plate 17B) contains a linear track of information, nearly five miles in length. Traditional audio
records have the spiral engraving record of the sound track.
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Objectives_template
Module 5 : Basic Paradigms
Lecture 11 : Torus, Coil, Helicoids, Spiral
TORUS Paradigm
Plate 8A Torus
8B Vehicle Tube & Tire
8D South Indian Medu Vada
(Source : http://www.google.co.in/search?hl=en&q=Tube+in+food&bav=on.2,or.r_gc.r_pw.r_qf.&biw=
1328&bih=574&um=1&ie=UTF8&tbm=isch&source=og&sa=N&tab=wi&ei=sNobUKz_OcbNrQfP4YDY
Cw#um=1&hl=en&tbm=isch&sa=1&q=Torus+shaped+products&oq=Torus+shaped+products&gs_l=
img.12...63.21515.5.23644.40.39.0.0.0.0.0.0..0.0...0.0...1c.kGHVxBkyb1Q&pbx=1&bav=on.2,or.r_gc.
r_pw.r_qf.&fp=76c868bca71bffed&biw=1328&bih=574; Aug 3,2012
A torus (plate 8A) is the shape mostly associated with vehicle tube filled with air or bangle. Besides the
inside negative space of the torus, there is also the space within (tubular) that might be functionally
important as well. Motor vehicle (plate 8B) tubes are having torus structure. Because of its structure it
could rotate around an axis. The formation of Medu Vada (plate 8D) is tubular structure. Because of the
hole inside the cooking becomes uniform from outside to inside which is similar to pasta.
Plate 9A Hula Hoop
9B Circle around an axis
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Objectives_template
Module 5 : Basic Paradigms
Lecture 11 : Torus, Coil, Helicoids, Spiral
(Source:http://www.google.co.in/search?hl=en&q=Tube+in+food&bav=on.2,or.r_gc.r_ pw.r_qf.&biw=
1328&bih=574&um=1&ie=UTF8&tbm=isch&source=og&sa=N&tab=wi&ei=sNobUKz_OcbNrQfP4YD
YCw#um=1&hl=en&tbm=isch&sa=1&q=Torus+shaped+vehicle+tire+%26+tube&oq=Torus+shaped+
vehicle+tire+%26+tube&gs_l=img.12...57557.67228.11.69120.14.14.0.0.0.0.0.0..0.0...0.0...1c.sMcpc
q0_ZUk&pbx=1&bav=on.2,or.r_gc.r_pw.r_qf.&fp=76c868bca71bffed&biw=1328&bih=574 ; Aug 3, 2012)
A circle or sphere moving radically around an axis (plate 9B) will describe a torus. If, for example, we
think of torus-shaped toy-the hula-hoop (plate 9A), and a marble inside the hoop, in the course of a
revolution around the hoop, the marble would travel the full interior space of the hoop based on the
principles of ‘law of motion’.
Plate 10A Inner Ear (cochlea)
10B Torus Shaped ‘Inner Ear’
Structure
10C Out, Middle & Inner Ear
(Source : http://en.wikipedia.org/wiki/Inner_ear ; Aug 3, 2012)
A related principle is employed in the human body to provide a sense of balance (equilibrium). If you
place sensors around the perimeter of the hula hoop that are triggered when touched by the marble,
you will have a device that can sense the orientation of hula-hoop, since gravity will draw the marble to
the lowest point in the hoop. If you place three such hoops at right angles to each other along imaginary
‘XY’, ‘XZ’ and ‘YZ’ planes (plate 10A), and you have a system that can detect almost any orientation.
This is nearly identical to structures that evolved as our sensory organs for position, the semicircular
canals located in the inner ear (plate 10B&C); the only significant differences are that the semicircular
canals are not quite perfectly torus-shaped, and liquid, rather than marbles, triggers the sensors.
(Read more: http://en.wikipedia.org/wiki/Inner_ear ; Aug 3, 2012; http://www.hooping.org/tag/hulahoop
-physics/ Aug. 19, 2012)
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Module 5 : Basic Paradigms
Lecture 11 : Torus, Coil, Helicoids, Spiral
COILS Paradigm
In most cases people mix up between coil and spiral. Coils and spirals are two closely related terms and
ideas. We interchange these two terms quite frequently. Isn’t it we usually say ‘snake coil’ and ‘spiral’
staircase? For the design purpose, though, we will define a coil as a series of loops of material that
is of more or less constant radius (plate 11A&B) as when wrapped around a cylindrical core,
whereas a spiral is made of loops that that steadily increase in diameter as they move outward
from the center (plate 11 C&D). A coil is more or less synonymous with a helix. If a coil is attached to a
core, as are the threads on a bolt, the term ‘helix’ is frequently used. Interestingly we do not realize the
basic difference in the paradigms of ‘coil’ and ‘spiral’.
Plate 11A Mechanical
Coil
11B Coiled Vine
11C Spiral Shell
11D Python Spiral
(Source : http://www.google.co.in/search?hl=en&q=Tube+in+food&bav=on.2,or.r_gc.r_pw.r_qf.&biw
=1328&bih=574&um=1&ie=UTF8&tbm=isch&source=og&sa=N&tab=wi&ei=sNobUKz_OcbNrQfP4Y
DYCw#um=1&hl=en&tbm=isch&sa=1&q=Spiral+Shell&oq=Spiral+Shell&gs_l=img.12...94240.9864
8.3.100746.7.7.0.0.0.0.0.0..0.0...0.0...1c.rIKjBYcUvJo&pbx=1&bav=on.2,or.r_gc.r_pw.r_qf.&fp=76c
868bca71bffed&biw=1328&bih=574 ; Aug 3,2012
Plate 12A Garden Hose Pipe
12B Coiled Electrical Wire
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12C Bottle Opener
Objectives_template
Module 5 : Basic Paradigms
Lecture 11 : Torus, Coil, Helicoids, Spiral
(Source :12A : http://www.google.co.in/search?hl=en&biw=1328&bih=574&q=coiled+hose+pipe&
bav=on.2,or.r_gc.r_pw.r_qf.&um=1&ie=UTF-8&tbm=isch&source=og&sa=N&tab=wi&ei=PpszUOu
aL47rrQeL6YHAAg ; Aug 21, 2012
12B : http://www.google.co.in/search?hl=en&q=Coiled+Electrical+wire&bav=on.2,or.r_gc.r_pw.r_qf.
&biw=1328&bih=574&um=1&ie=UTF-8&tbm=isch&source=og&sa=N&tab=wi&ei=bZ0zULupKI3QrQ
fNsYHoCA ; Aug 21, 2012
12C : http://www.google.co.in/search?hl=en&q=Coiled+Cork+Opener&bav=on.2,or.r_gc.r_pw.r_qf.
&biw=1328&bih=574&um=1&ie=UTF8&tbm=isch&source=og&sa=N&tab=wi&ei=mZ4zUIeTN83tr
Qe4yYCQBA ; Aug. 21, 2012)
Coils are found in nature quite commonly. Coil is frequently applied in design. Coils are a compact form
for long things (plate 12A-C). Long things can be stored by coiling them. Climber plants (plate 11B),
such as grape plants, cucumbers, and peas, have coiled tendrils that tend to catch onto things to
support the climbing plants. In nature the climbing plants has to have some kind of support for support.
Using the same principle man has cleverly designed coiled wires to store longer wire in a compact
condition, such as rope, electrical wire (plate 12B), hoses (plate 12A), etc. can be stored in compact
manner in a smaller area. The word ‘coil’ comes from the French word cuillir, ‘to gather’. Coils behave
differently when turned than when pulled; for instance, a corkscrew (plate 12C) when turned will enter
inside the cork, and when pulled it pulls out the cork. Coils also act like as springs (plate 11A), when
they are both pulled apart and pushed together. Mechanical Coiled Springs are commonly used in many
products. Coiling is commonly used for long power cords (plate 12B) for various appliances, such as
telephone, computer, etc.
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Objectives_template
Module 5 : Basic Paradigms
Lecture 11 : Torus, Coil, Helicoids, Spiral
Plate 13A Coil Spring
13B Tendrils Holding
13C Door Closer Coil Spring
(Source : 13A : http://www.google.co.in/search?hl=en&q=Coil%20spring&bav=on.2,or.r_gc.r_pw.r_
qf.&biw=1328&bih=574&noj=1&um=1&ie=UTF-8&tbm=isch&source=og&sa=N&tab=wi&ei=T8IzUL
_hL9HOrQevrYDAAg
13B : http://www.google.co.in/search?hl=en&q=climber%27s+tendrils&bav=on.2,or.r_gc.r_pw.r_qf.&
biw=1328&bih=574&um=1&ie=UTF-8&tbm=isch&source=og&sa=N&tab=wi&ei=b8AzUO76Ls3RrQf
97YDYDA ; Aug. 21, 2012
13C : http://www.google.co.in/search?hl=en&q=Door+Coil+spring&bav=on.2,or.r_gc.r_pw.r_qf.&biw=
1328&bih=574&um=1&ie=UTF8&tbm=isch&source=og&sa=N&tab=wi&ei=f8UzUKXJK4HNrQe7k4Bw
#um=1&hl=en&tbm=isch&sa=1&q=Door+close+spring&oq=Door+close+spring&gs_l=img.12...60670
.61851.0.64094.5.5.0.0.0.0.0.0..0.0...0.0...1c.B_vvwiNFDU&pbx=1&bav=on.2,or.r_gc.r_pw.r_qf.&fp=
e2ad3fd6e808f277&biw=1328&bih=574 ; Aug. 21, 2012)
Coil form has some properties that make it well suited to springs. It is used as shock absorbing
suspension device (plate 13A) for motor vehicle to various machines. Coil form can bear the weight of
an object while in compressed position and returns to the original position once the object is lifted from
the place. The elasticity of the material in coil allows spreading out the deformation. It provides a range
within which the material is able to snap back to its original form. The coil in nature similarly holds the
tendrils (plate 13B) as support to climbing. Door closer coil-spring (plate 13C) is used for automatic door
closing.
Helicoids
Helicoids are an extension of the Coil Paradigm. Helicoids may be visualized as a helix, oriented
vertically, and centred around the z-axis, with each point on the helix connected to the axis by a line
parallel to the x-y plane (plate 12C).
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Objectives_template
Module 5 : Basic Paradigms
Lecture 11 : Torus, Coil, Helicoids, Spiral
Plate 12A Screw Design
12B Helicoids
12C Screw
12D Helicoids
Structure
(Source : http://www.google.co.in/search?hl=en&q=About+Helicoids&bav=on.2,or.r_gc.r_pw.r_qf.&
biw=1328&bih=574&um=1&ie=UTF8&tbm=isch&source=og&sa=N&tab=wi&ei=0jUdUNaaFMforQeV
7IHQDA ; Aug 4, 2012)
(Read more: http://en.wikipedia.org/wiki/Screw_thread ; Aug. 22, 2012)
“The Archimedes' screw consists of a screw (a helical surface surrounding a central cylindrical shaft)
inside a hollow pipe.” (Ref. http://en.wikipedia.org/wiki/Archimedes%27_screw ; Aug. 22, 2012)
The Archimedes' screw consists of a screw (a helical surface surrounding a central cylindrical shaft)
inside a hollow pipe. “A screw thread (plate 12B-D), often shortened to thread, is a helical structure
used to convert between rotational and linear movement or force. A screw thread is a ridge wrapped
around a cylinder or cone in the form of a helix, with the former being called a straight thread and the
latter called a tapered thread. A screw thread is the essential feature of the screw as a simple machine
and also as a fastener. More screw threads are produced each year than any other machine element.
[1]” (Ref. http://en.wikipedia.org/wiki/Screw_thread ; Aug. 22, 2012)
Because of its unique of screw it is being used in various products for thousands of years. The angle of
the thread (‘V’) is standardized as 60 degree. However there is no restriction to any other angle.
Plate 13 Helicoids Shaped Staircase
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Objectives_template
Module 5 : Basic Paradigms
Lecture 11 : Torus, Coil, Helicoids, Spiral
(Source : http://www.google.co.in/#hl=en&output=search&sclient=psyab&q=Spiral+Staircase&oq=
Spiral+Staircase&gs_l=hp.12...217.870.0.2992.4.4.0.0.0.0.0.0..0.0...0.0...1c.qL8ha0mgbrg&pbx=1&
bav=on.2,or.r_gc.r_pw.r_qf.&fp=13f6aaee78637b17&biw=1328&bih=574 ; Aug 4, 2012)
A spiral stairs (plate 13) is actually helicoids shape, as well as variations on the screw auger. The Greek
mathematician, astronomer and philosopher Archimedes (285-212 BC) is generally credited with the
developing the Archimedes Screw (plate 12B), a device that is used to raising groundwater from
the well. Traditionally the same technique is used for irrigation, extracting water from well or for tilling
soil.
Plate 14A Archimedes’s Screw
‘Rural Well’, India (Helicoids)
14B Water well, Punjab
14C Harvest and Tilling
The Archimedes Screw is helicoids within a cylinder tilted at about 45-degree tilt. As the screw is turned,
pockets in the form move steadily upward. The device (plate 14A&B) is widely used in the rural India for
pumping water from the community well and in agriculture and also for tilling the soil (plate 14C). The
advantage of the device is it is resistant to clogging. The same application is used for moving grain and
controlling the flow of materials from hoppers. Extracting water from lower heights (plate 15A) the
Archimedes Screw is widely used in the agriculture sectors. It is one of the classical traditional
techniques that are used around the world for centuries.
Plate 15A Archimedes Screw for drawing
15B Dutch Windmill 15C Hydro Turbine
Groundwater
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Objectives_template
Module 5 : Basic Paradigms
Lecture 11 : Torus, Coil, Helicoids, Spiral
(Ref. http://en.wikipedia.org/wiki/Archimedes%27_screw ; Aug 4, 2012)
(Source : http://www.google.co.in/search?hl=en&q=Archimedes+Screw+in+Harvest&bav=on.2,or.r_g
c.r_pw.r_qf.&biw=1328&bih=574&um=1&ie=UTF8&tbm=isch&source=og&sa=N&tab=wi&ei=ebUcUJf
XEobnrAfV4HwBw#um=1&hl=en&tbm=isch&sa=1&q=Archimedes+Screw+in+Windmill&oq=Archime
des+Screw+in+Windmill&gs_l=img.12...96.11259.40.13374.12.12.0.0.0.0.0.0..0.0...0.0...1c.98EE2bB
CeY0&pbx=1&bav=on.2,or.r_gc.r_pw.r_qf.&fp=340b07ee0ef1dc5f&biw=1328&bih=574 ; Aug 4, 2012
15B : http://www.texva.com/holland/The%20Dutch%20Windmill.htm ; Aug. 22, 2012
“The Archimedes' screw, also called the Archimedean screw or screw-pump, is a machine
historically used for transferring water from a low-lying body of water into irrigation ditches. The screw
pump is commonly attributed to Archimedes on the occasion of his visit to Egypt, but this tradition may
reflect only that the apparatus was unknown before Hellenistic times and introduced in his lifetime by
unknown Greek engineers.”
(Ref. http://en.wikipedia.org/wiki/Archimedes%27_screw ; Aug 4, 2012)
In modern time the same principle is applied for generating electricity from Hydro Turbine (pale 15B) as
Green Energy in many Europe. The Netherlands is successfully using the same technique for long time
in ‘windmill’ and in hydro turbine’ (plate 15B&C) projects. It is one of the most successful green-energy
techniques that are used in various ways through innovative ideas around the world.
SPIRAL Paradigm
Spirals are closely related to coils, but a spiral usually starts at a center point and winds outward,
gradually increasing the radius (plate 16A & B).
Plate 16A Fibonacci Spiral
16B Spiral
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16C Spiral- Climber