ME 160 SECTION 5.1 OF CHAPTER 6 PRINCIPLES OF DEVELOPMENT

Summary

The video script from NP one six zero engineering covers the principles and methods of surface development in engineering graphics. It explains the classification of solids into polyhedra and solids of revolution, including right and oblique solids like cylinders, cones, and prisms. The script delves into types of solid surfaces, such as plane, single curved, and convoluted surfaces, highlighting their development principles. It outlines various development methods like the power line method, radial line method, triangulation method, and approximation method, emphasizing the importance of understanding surface types and positions for accurate surface development. The goal is to produce a flat pattern that reflects the true shape and dimensions of the solid, crucial for manufacturing processes.

Takeaways

• 📚 The video script discusses the principles of surface development in engineering graphics, focusing on the methods used to represent three-dimensional solids on a two-dimensional plane.
• 🔍 Solids are categorized into two main types: polyhedra and solids of revolution, with further classification into right and oblique solids based on the orientation of their axes.
• 📏 The script explains how to represent right and oblique cylinders and cones through orthographic projections, emphasizing the importance of the axis's orientation relative to the base.
• 📐 Prisms are differentiated into right and oblique based on whether their lateral edges are perpendicular to the base, which affects how their surfaces are developed.
• 🌐 Surfaces of solids are classified into plane, single curved, and double curved surfaces, each with distinct methods of representation and development.
• 🛠 Developable surfaces can be unfolded into a flat shape without distortion, including planes, single curved surfaces, and certain combinations thereof.
• 📈 The process of surface development involves identifying suitable lines on the solid, determining their true lengths through auxiliary projection methods, and then unfolding the surface.
• 📝 Accurate surface development requires knowledge of the type of surface, its shape, position relative to a reference, and the method of development to be used.
• 🔧 The script outlines various methods for surface development, including the power line method, radial line method, triangulation method, and approximation method.
• 📉 The outcome of surface development should include a pattern of the developed surface with true lengths and shapes, as well as information on the openness of the solid and dihedral angles between plates.
• 👨‍🏫 The video aims to educate viewers on the principles and practices of surface development in engineering, providing a comprehensive guide to understanding and applying these concepts.

Q & A

What are the main objectives of the NP one six zero engineering lecture?

The main objectives are to understand the principles of surface development and to apply various methods such as the press the power line method, the radial line method, the applied triangulation method, and the approximation method.

How are solids generally classified in engineering graphics?

Solids are generally classified as polyhedra and solids of revolution. They may also be classified as right solids or oblique solids.

What is a right cylinder and how can it be identified in a drawing?

A right cylinder is a solid where its axis (Oz) is perpendicular to the base. It can be identified by a drawing showing the base or lower opening giving the diameter and the axis being perpendicular to that path.

What is an oblique cylinder and how does it differ from a right cylinder?

An oblique cylinder has its axis inclined to its base. It differs from a right cylinder in that the diameter and the cross-section are not perpendicular to the base, resulting in an elliptical cross-section instead of a circular one.

How is a right cone or pyramid different from an oblique cone or pyramid?

A right cone or pyramid has its axis perpendicular to its base, whereas an oblique cone or pyramid has its axis inclined to the base, and the height is also inclined, not perpendicular.

What are the three categories of solid surfaces in engineering practice?

The three categories of solid surfaces are plane surfaces, single curved surfaces, and double curved surfaces.

Can you provide an example of a single curved surface?

An example of a single curved surface is a cylindrical surface, which is curved along one axis and straight along the other.

What is a developable surface and why are they important in surface development?

Developable surfaces are surfaces that can be unfolded into a flat plane without stretching or distortion. They are important because they allow for accurate representation of the surface in a two-dimensional form.

What are the four methods used in surface development mentioned in the script?

The four methods used in surface development are the press the power line method, the radial line method, the applied triangulation method, and the approximation method.

What are the outcomes of the surface development processes?

The outcomes of the surface development processes are the pattern of the developed surface with true lengths and true shapes, the true shapes of the lower and upper sections (openings), and the dihedral angles between plates.

Why is it necessary to know the type of surface and its position before developing it?

Knowing the type of surface and its position is necessary to select the appropriate method of development and to ensure that the developed surface accurately represents the three-dimensional shape in a two-dimensional form.

Outlines

00:00

📚 Principles of Surface Development and Solid Types

This paragraph introduces the fundamental concepts of surface development in engineering graphics, focusing on the principles and methods used to represent three-dimensional solids on a two-dimensional plane. It explains the types of solids, such as polyhedra and solids of revolution, and further classifies them into right and oblique solids. The paragraph provides examples of right and oblique cylinders, cones, and pyramids, detailing their characteristics and how they are represented in drawings. The importance of understanding the orientation of the axis (Oz) and the base, as well as the cross-sectional shapes, is emphasized for accurate solid representation.

05:03

🏗️ Types of Solids and Surfaces in Engineering Graphics

The second paragraph delves into the classification of solid surfaces in engineering practice, which are categorized into plane surfaces, single curved surfaces, and double curved surfaces. It provides examples of plane surfaces, such as the surfaces of a prism, and single curved surfaces, like a cylinder. The paragraph also discusses conical surfaces and convoluted surfaces, explaining how they are formed and their characteristics. Additionally, it introduces the concept of developable surfaces, which can be unfolded into a flat shape without distortion, and non-developable surfaces that require approximation methods for representation.

10:03

🛠️ Surface Development Techniques and Their Applications

The final paragraph outlines the procedures and methods used in surface development, which is the process of creating a flat pattern from a three-dimensional surface. It discusses the importance of knowing the type of surface, such as plane, cylindrical, conical, or web surfaces, to apply the correct development technique. The paragraph explains that developable surfaces can be unfolded without distortion, while non-developable surfaces require approximation. It also highlights the methods used in surface development, including the power line method, radial line method, triangulation method, and approximation method. The outcome of the development process is a pattern that shows the true lengths and shapes of the surface, including the necessary dihedral angles and open sections for construction purposes.

Keywords

💡Surface Development

Surface development refers to the process of creating a flat pattern from a three-dimensional solid surface, which is essential in engineering and architecture for manufacturing and construction purposes. In the video, different methods such as the press the power line method, radial line method, triangulation method, and approximation method are discussed to apply to various types of solids. The script mentions that the principles of surface development involve identifying types of solids and their surfaces, which is central to the video's theme.

💡Solids of Revolution

Solids of revolution are three-dimensional shapes formed by rotating a two-dimensional shape around an axis. In the script, examples like right and oblique cylinders and cones are given, where the axis of rotation is either perpendicular or inclined to the base. This concept is integral to understanding how surfaces can be developed from solids that have been created through a rotational process.

💡Right Cylinder

A right cylinder is a geometric solid with two parallel and congruent circular bases, connected by a curved surface. The axis of the cylinder is perpendicular to its bases. In the script, the right cylinder is used to illustrate the application of surface development principles, showing how the diameter and cross-section can be used to represent the solid in two-dimensional drawings.

💡Oblique Cylinder

An oblique cylinder is similar to a right cylinder but with its axis inclined to the base. This means the axis is not perpendicular to the bases, resulting in elliptical cross-sections instead of circles. The script explains how to identify an oblique cylinder by its inclined axis and elliptical cross-sections, which is crucial for accurate surface development.

💡Right Cone

A right cone is a solid with a circular base and a vertex, where all elements are connected by a sloping surface that converges at the vertex. The script describes a right cone as having a height that is perpendicular to its base, which is important for understanding how the cone's surface can be developed into a flat pattern.

💡Oblique Cone

An oblique cone is characterized by its vertex not being perpendicular to the base, resulting in a slanted height and an elliptical base. The script uses the oblique cone to demonstrate how the angle of the axis affects the shape's development, which is essential for accurately depicting the cone in two dimensions.

💡Prism

A prism is a polyhedron with two congruent and parallel faces (called bases) and other faces (lateral faces) that are parallelograms. The script distinguishes between right prisms, where the lateral edges are perpendicular to the base, and oblique prisms, where they are not, which affects the method of surface development.

💡Developable Surfaces

Developable surfaces are those that can be unfolded into a flat shape without distortion. The script mentions that planes, single curved surfaces, and combinations thereof are developable. This is important because it determines the ease and accuracy with which a surface can be developed from a three-dimensional solid.

💡Development Methods

The script outlines various methods for surface development, including the press the power line method, radial line method, triangulation method, and approximation method. Each method is suited to different types of surfaces and solids, and understanding these methods is key to successfully developing surfaces for practical applications.

💡Auxiliary Views

Auxiliary views are additional projections used in technical drawing to provide a clearer representation of the object. The script suggests using auxiliary methods of life projection to determine the true length of lines on the solid, which is necessary for accurate surface development.

💡Truncation

Truncation refers to the process of cutting off a portion of a solid, as exemplified by a truncated cone in the script. This concept is important in surface development as it affects the shape and size of the resulting flat pattern, especially when dealing with complex solids.

Highlights

Introduction to principles of surface development in engineering graphics.

Understanding different types of solids: polyhedra and solids of revolution.

Identification of right and oblique solids, including cylinders, cones, and pyramids.

Explanation of right cylinder characteristics and how to identify them.

Application of principles for connecting right cylinders in engineering.

Identification of oblique cylinders through their inclined axes and elliptical cross-sections.

Differentiation between right and oblique cones or pyramids based on their axes and base relationships.

Description of right prisms and their perpendicular lateral edges to the base.

Introduction to oblique prisms with lateral edges not perpendicular to the base.

Classification of solid surfaces into plane, single curved, and double curved surfaces.

Examples of plane surfaces produced by moving a line along parallel lines.

Explanation of single curved surfaces like cylindrical surfaces.

Description of conical surfaces with their horizontal bases and curved profiles.

Introduction to convoluted surfaces with tangent line control and double curve directrix.

Concept of developable surfaces that can be unfolded into a flat shape without distortion.

Process of surface development including identifying types of surfaces, their positions, and development methods.

Different methods of surface development: power line method, radial line method, triangulation method, and approximation method.

Outcomes of the development process, including patterns, true lengths, and shapes of surfaces.

Transcripts

welcome to NP one six zero engineering

growing at six development six learning

objectives past six one understand the

principles of surface development to

apply the press the power line method

three apply the radial line method for

applied triangulation method and five

the approximation method but six six

point one six point one principles of

surface development objectives identify

types of solids identify types of solid

surfaces and also explain the principle

of surface development types of solid in

engineering graphics solids are

generally classified as one polyhedra

and two are solids of revolution they

may also be classified as one right

solid or be oblique solids types of

solid right cylinder its Oz's is

perpendicular to each space here we have

a picture we have a drawing through the

elevation the base or the lower opening

gives us the diameter and if other since

perpendicular to that path so is a right

prism the cross section which is a cut

through that portion here and it is

circular in nature

now the second view shows that cut

portions of the same right triangle this

time again they're done without

specifying the actual cross section of

it so the top open is an elliptic in

nature and then we have the cross

section which is also going to be

circular cross-section now at a view

represented pre representing a cylinder

slanting on the top ends as well as the

lower ends here however the diameter

measured here is given and the cross

session also specifies the circular

cross-section and the top opening and

lower open an ellipse of the same type

right cylinder here we have an example

of application of rice cylinders being

connected how do we see it the diameter

which shows that it is a right cylinder

because it is perpendicular the others

are dependent not related

oblique cylinder for an oblique cylinder

it has his ass's inclined to its base

the base does the diameter being

specified over here so and note the

cross section here is no longer a

segment but ellipse shaped again the

same figure this time let's take the

diameter which is the opening

corresponding to the true shape of the

opening and here the cross section is

going to be their electrical cross

section then again the same thing the

same view as the previous one but this

time the dimension diameter this across

here so it is an oblique cylinder the

diameter does a cross section through

that object to give us an ellipse shape

let's look at another example typical

occasion this time why is it an oblique

cylinder the diameter opening does a

lower opinion is the diameter not the

middle so the Oz's

is inclined to that Oakley so it is

uncle Blake cylinder right cone or

pyramid it's athis is perpendicular to

its base here we have the height the

Vettes the height

and a path along which it goes and that

is the base and we see here it is

perpendicular to it now here we have our

coal which is a suspect and accredit

diameter is the base over here defined

likewise we look at this drawing over

here here we have is a truncated cone

which has been cut out with portions of

the cut off portion shown in red but

looking at the diameter as it is from

the be sticking from here that is how it

has been formed therefore this is a

right triangle a right chord

now let's look at at oblique cone or

pyramid here again we have this showing

now if you look at this that is they

kept the base of it as such and others

of the others of the coal which is

inclined to the base and the height is

also inclined as it is to the others not

as it is here we have that cone shown

are in Detroit and clearly the diameter

identified here is D different from this

over here this is a sacra lower or P and

therefore existing client and therefore

an oblique corn right prisoner a prison

has its axis perpendicular to its base

the lateral H that is the lateral h

right the lateral edge of the prism is

perpendicular to its base Athens's now

take a look at an oblique prism now the

lateral edge is not perpendicular to the

base so it is an oblique prism types of

solid surfaces what in engineering

practice practice surfaces of solids

fall into three categories root surfaces

what surfaces and mobile curved surfaces

a root surface can be produced by moving

a line along a straight or curved paths

let's see examples of Google surfaces

now the plane surface the plane surface

is a situation where you have a line a B

and you move it along two parallel lines

X Y and this is the result of a claim as

this lines moves along on it moves along

it typical examples are the surfaces of

a prism then let's look at a second

example sample that is a single curved

surfaces single curved surface is a

typical example is the cylindrical

surface whereby cylindrical shape wise

we have it curved along one particle at

end of it like what we have over here is

a single curved surface power lines kept

around now here it shows the two views

that is the elevation and this is the

plan of the line and under curve so here

is a straight curve and here can be

another curve that is that is here sorry

this is a curve at a base but it is

horizontal just like we have here that

is our curve but it's on a horizontal

base so there it will be a line and here

to show the curve corresponding to that

here we have a son laughing over here a

typical example is the cylinder now

let's look at the conical surface in the

case of the conical surface that is a

horizontal base so the elevation of it

is going to be and straight horizontal

line but a cab itself is hassle nature

here which the top view as we see the

curve of it and now the point that is a

line a B which prescribes moves on this

curve but our trail restricts itself

through a park wa points s over here so

you can see in moving through it always

passes through that Vectis that is the s

point to give us the result a typical

example is the cool

now let us look at a convoluted surface

the convolute surface is one there are

two types that tangent control it and

end sorry the tangent line convoluted

and at a tangent play covered in that

tangent line coverlet you normally have

a double curve directrix that means it

has to care of situations one on the

plane that to be secular and another or

other side rising up so it's double

curve directrix the line that we move

along these directories must be tangent

to that line so for all situations is

dysfunction to it now in the other

situation that is our directrix her

Avadh are two of them however here the

line lies on a plane which is tangential

to the directrix here you have directrix

there are two of them and this plane is

always tangential today two and our line

must lie on that plane tangent plane

confident now it's the sector B what

surface what surface is a root surface

for which twos successive elements I

neither power nor pass through a common

point that is the opposite of what we

have for the plane as well as what that

we have for the single curve situation

it's not here example here we have this

web surfaces which is shown over here

but will not take this as part of our X

now types of celestial double care

surface that is generated by revolving a

curved line about a straight line in the

plane of the curve the straight line is

passes typical examples are for example

here we have the others that's our

straight line and we have our curve

which is a circle over here of radius

small R in the cutter

for various relationship between kata

are as more are here for Kappa are being

greeted and small we have a tourist for

Kappa I'll be laser small are we have a

clue store tourists and where are Kappa

are is got to zero we have a sphere

development involves through lips to

length of the lines required knowledge

of one the type of surface example plane

surface cylindrical surface conical or

web surface must be known to the ship of

the surface one it can be triangular

square etc then three position of the

surface is very important because we

have to develop surface to surface

position relative to a reference of free

so on edge principle surface development

for development principle surface

development we should differentiate

developable surfaces which are surfaces

that may be unfolded on on route through

life flat then we call those surfaces

developable surfaces the true

developmental true development involve

no stretching or distortion of the

surface planes single curved surfaces or

combinations of combinations of these

are developable however worked and

double curved surfaces are not directly

developable they involve distortion and

in straw stretching of the object

procedure of development one introduce

suitable lines onto the surface on the

solid to which you can achieve by the

method of development then to determine

the true length of these lines that is

by auxillary method of life projection

or

methods then free cut open along aligned

and normally with the shortest through

length or located after convenient

Porsche shall we select a line at a

convenient position such as the welding

they're bringing together office bring

it to get out there edges will give us a

form which is beautiful then also to

after you've cut open you should be able

to unfold the pieces to lie flat lots of

development the fully metals are

involved in surface development our line

method radial line method triangulation

method and approximation method the

outcome of development processes are one

the pattern of the developed surface

with the true lengths and true ships of

the surface is shown to true shapes of

the lower and upper sections which are

the openness if not provided must be

given and three dihedral angles between

plates must also be provided thank you

packed off thank you for end of Pat 6.1