AESTHETIC EDUCATION10TH GRADE: Q2P1Materials: A4 white cardboard, 2h pencil, compass, ruler, set squares.

CIRCLE’S IMPORTANT LINES:

Because people have studied circles for thousands of years special names have come about.

A circle is a round, two dimensional shape that looks similar to the letter ‘O’.

All points on the edge of a circle are the same distance to the center.

The circumference of a circle can be found with the following formula: Circumference = π d

The area of a circle can be found with the following formula: Area = π r²

RADIUS: A straight line from the center of a circle to

the edge is called the radius.

DIAMETER A straight line that passes from one side of a

circle to the other through the center is called the diameter.

CIRCUMFERENCE The distance around the outside of a circle is

called the circumference.

ARC An arc is part of the circumference of a

circle.

CHORD A chord is a straight line joining two points

on a circle, the diameter is an example of a chord (the longest possible one).

TANGENT A tangent is a straight line that touches a

single point of a circle.

SECANT A secant is a line passing through two points

of a curve.

THE AREAS INSIDE A CIRCLESEGMENT A segment is the region between a chord

and the arc it joins.

SECTOR A sector is the region between an arc and

two radius.

TANGENT (LINE)

A line that touches a curve at a point without crossing over.

1. DRAW A LINE TANGENT TO A CIRCLE

1. Draw an AB circumference with a diameter of 8cm.

2. Place the O at the center of that circumference.

3. Center at A, and with an opening from A to O, draw an arc that cut the circumference, place point C.

4. Draw a line from O to C, and extend the line.5. Center at C, set the opening of the compass

from C to A and draw a semicircumference, and start from A and cut the extended line. Place point D.

2. DRAW A CIRCLE TANGENT TO A LINE

1. Draw an AB segment of 8cm, and place point P anywhere on the segment.

2. Center at P and draw a semicircumference that cut the AB segment at two points, place point 1 and 2.

3. Center at 1, with an opening from 1 to 2 draw and arc above the AB segment, repeat from 2. Place the point 3.

4. Draw a line from P to 3, place point 4 where the recently drawn line intersect with the semicircumference.

5. Center at 4, draw a circumference with a radius from 4 to P.

AESTHETIC EDUCATION10TH GRADE: Q2P1Materials: A4 white cardboard, 2h pencil, compass, ruler, set squares.

CLASSICAL MOLDINGS

Molding, or moulding (Commonwealth), also known as coving (UK, Australia), is a strip of material with various profiles used to cover transitions between surfaces or for decoration. It is traditionally made from solid milled wood or plaster, but may be made from plastic or reformed wood. In classical architecture and sculpture, the molding is often carved in marble or other stones.

An ornamentally shaped outline as an architectural feature, especially in a cornice.

Used as a decoration on frames, tables, and certain architectural members, as cornices, stringcourses, or bases.

At their simplest, moldings are a means of applying light- and dark-shaded stripes to a structural objects without having to change the material or apply pigments. The contrast of dark and light areas gives definition to the object.

Types

There are a variety of common moldings:

Astragal A small convex molding.

A semi-circular molding attached to one of a pair of especially fire doors to cover the air gap where the doors meet.

Bead A convex molding, usually semi-circular. There are a variety of different types of beads. Examples include: angle bead, nosing bead, double bead and so forth.

Narrow, half-round convex molding, when repeated forms reeding.

Beak Molding shaped into a beak-like form. Small fillet molding left on the edge of a Larimer, which forms a canal, and makes a kind of pendant.

Cavetto (Italian) cavare: "to hollow", concave, quarter-round molding sometimes employed in the place of the cymatium of a cornice

Congé A concave molding.

Cyma is a moulding with a double curvature is called a cyma or sometimes, a wave moulding. Used as the uppermost element in a cornice.

Cyma Recta A cyma moulding having an upper concave curve and a lower convex curve Cyma Recta – igoca

Cyma Reversa A cyma moulding having an upper convex curve and a lower concave curve.

Fascia A flat horizontal surface. In classical architecture, fascia are often used in multiple bands, each projecting beyond the one below.

Fillet A narrow band with a vertical face. Fillets are often interposed between curved mouldings.

Fillet, Sunk A fillet that is depressed between two other architectural elements.

Fluting Vertical, half-round grooves cut into the surface of a column in regular intervals, each separated by a flat astragal.

Ovolo A convex moulding, among woodworkers it is referred to as a "quarter round."

Reed Sometimes called reed moulding or reeding, a series of convex mouldings running parallel.

Scotia A concave molding between two fillets. A scotia is one of the elements used in the Attic base of columns.

Concave molding with a lower edge projecting beyond the top and so used at the base of

columns as a transition between two torus moldings with different diameters

Three-quarter Hollow Moulding shaped by a three-quarter concave profile.

Three-quarter Moulding shaped by a three-quarter convex profile. Three-quarter

Thumb Molding Thumb-shaped Molding

Torus A semi-circular, convex molding. The torus is one of the distinctive elements in the Attic base used by columns in classical architecture.

AESTHETIC EDUCATION10TH GRADE: Q2P2 (Part1)

Drawing Tools to be used:

Compass, pencil, rulers, eraser, markers and a properly framed A4 cardboard.

PARALLEL LINES

Lines are parallel if they are always the same distance apart (equidistant), and will never meet.

PERPENDICULAR BISECTOR.

A perpendicular bisector is a line segment perpendicular (90 degrees angle) to AB and passing through the midpoint (M) of AB.

ANGLE BISECTOR

The (interior) bisector of an angle, also called the internal angle bisector, is the line or line segment that divides the angle into two equal parts.

ARCHES

What is an ARCH?

Arch, in architecture and civil engineering, is the structural element that have a curved shape that is used to span an opening and to support loads from above. The arch formed the basis for the evolution of the vault.

Arch construction depends essentially on the wedge. If a series of wedge-shaped blocks—i.e., ones in which the upper edge is wider than the lower edge—are set flank to flank in the manner shown in the figure, the result is an arch. These blocks are called voussoirs. Each voussoir must be precisely cut so that it presses firmly against the surface of neighboring blocks and conducts loads uniformly. The central voussoir is called the keystone. The point from which the arch rises from its vertical supports is known as the spring,

or springing line. During construction of an arch, the voussoirs require support from below until the keystone has been set in place; this support usually takes the form of temporary wooden centring. The curve in an arch may be semicircular, segmental (consisting of less than one-half of a circle), or pointed (two intersecting arcs of a circle); noncircular curves can also be used successfully.

What is an ARCH function?

It has the function to transmit loads to the walls or pillars that support it.

Centring or Falsework

Falsework, also called Centring, temporary construction to support arches and similar structures while the mortar or concrete is setting or the steel is being joined. As soon as the work is set, the centring is carefully removed; this process is called striking the centring. The same method is used in building brick sewers. The name centring originated from the primary use in centred arches.

ARCADE

Arcade, in architecture, a series of arches carried by columns or piers, a passageway between arches and a solid wall, or a covered walkway that provides access to adjacent shops. An arcade that supports a wall, a roof, or an entablature gains enough strength from lateral thrusts that each individual arch exerts against the next to carry tremendous weight loads and to stretch for great distances.

Ancient aqueducts show an early use of the arcade. Later Roman builders used the pattern to construct large wall surfaces: the Colosseum, with 80 arcaded openings on each of its three stories, is one of the finest examples of this architectural form.

VAULT

A roof in the form of an arch or a series of arches, typical of churches and other large, formal buildings

Four common types of vault. A barrel vault (also called a cradle vault, tunnel vault, or wagon vault) has a semicircular cross section. A groin (or cross) vault is formed by the perpendicular intersection of two barrel vaults. A rib (or ribbed) vault is supported by a series of arched diagonal ribs that divide the vault’s surface into panels. A fan vault is composed of concave sections with ribs spreading out like a fan.

DOME

Domes appeared first on round huts and tombs in the ancient Near East, India, and the Mediterranean region but only as solid mounds or in techniques adaptable only to the smallest buildings.

They became technically significant with the introduction of the large-scale masonry hemispheres by the Romans. Domes, like vaults, evolved from the arch, for in their simplest form they may be thought of as a continuous series of arches, with the same center. Therefore, the dome exerts thrusts all around its perimeter, and the earliest monumental examples required heavy walls. Since the walls permitted few openings and had to be round or polygonal to give continuous support, early domes were difficult to incorporate into complex structures, especially when adjacent spaces were vaulted.

PRINCIPAL PARTS

IntradosThe inner curve of an arch is called as intrados.

ExtradosThe outer curve of an arch is termed as extrados.

VoussoirsThe wedge-shaped units of masonry which are forming an arch is called as voussoirs.

Crown of an ArchThe highest part are peak point of extrados is called crown.

KeystoneThe wedge shaped unit which is fixed at the crown of the arch is called keystone.

Spandrel in an Arch:If two arches are constructed side by side, then a curved triangular space is formed between the extrados with the base as horizontal line through the crown. This space is called as spandrel.

Pier and Abutment of an ArchThe intermediate support of an arch is called as pier. The end support of an arch is called as abutment.

Skew Back

This is an inclined surface or splayed surface on abutment, from which arch curve starts or ends.

Springing PointsThe imaginary points which are responsible for the springing of curve of an arch are called as springing points.

Springing LineThe imaginary line joining the springing points of either ends is called as springing line.

Springer in ArchesThe first voussoir at springing level which is immediately adjacent to the skewback is called as springer.

ImpostThe projecting course is provided on the upper part of a pier or abutment to stress the springing line. This course is called impost.

Span of an ArchThe clear horizontal distance between the supports or abutments or piers is termed as span of an arch.

Rise of an ArchThe clear vertical distance between the highest point on the intrados and the springing line is called as rise.

ARCHESUNEQUAL ROUND ARCH.

1. We draw to parallel lines, Line AB= 8 cm and line CD = 6 cm. the separation between them is 6 cm

2. Then we draw perpendicular lines to A and C, mark pint E.

3. Extend the line CD and mark point F.4. Then with C as a center and an opening to F

we draw an arch to get the point G.5. Then we obtain the perpendicular bisector of

EG and we extend the result beyond AF.6. Mark the new points 1 and 2.7. Center in 1, and draw the first part of the arch

with an A-1 opening. Until it reaches the previous perpendicular bisector.

8. Then making center in 2 and an opening C-2 finish the UNEQUAL ROUND ARCH.

ROUND ARCH

1. We draw to parallel lines, 7cm each and with 6 cm separation.

2. Mark point A and B at the top of the two lines.

3. Then we obtain the perpendicular bisector of AB

4. Then making center in C and with radius AC, we draw the arch.

GOTHIC ARCH

1. We draw to parallel lines, 6cm each and with 6 cm separation.

2. Mark point A and B at the top of the two lines.

3. Then we obtain the perpendicular bisector of AB, mark point C and we extend the resulting line.

4. Obtain the perpendicular bisector of AC, and mark point D.

5. Obtain the perpendicular bisector of BC, and mark point E.

6. We center in D, and we draw an arch with a BD opening. Until it reaches the extended middle line.

7. Then we do the same from the point E, we draw an arch with an AE opening, and finish de arch.

AESTHETIC EDUCATION10TH GRADE: Q2P2 (Part2)

Drawing Tools to be used:Compass, pencil, rulers, eraser, markers and a properly framed A4 cardboard.

OVAL: Oval is a closed and flat curve, composed of four arcs of circumference, equal two to two. It has two axes of symmetry perpendicular to each other.

Construction of ovals: Below you will find ovals’ most used construction procedures in technical drawing.

OVAL KNOWING THE MINOR AXIS.

1. We draw a vertical line CD of 6cm.2. Find the perpendicular bisector for CD, place

point O at the middle point.3. Using point O, draw a horizontal line

(perpendicular to CD), this line will be as long as needed. Place point A and B on each end.

4. Using O as the center and with an opening from O to C, draw a circumference that cuts the horizontal line (mayor axis), on that cuts place point O1 and O2.

5. With the ruler, draw straight lines from C and D to O1 and extend the lines beyond.

6. Repeat, now for point O2 from C and D.7. Now center at D, with an opening from D to

C, draw a large arc until each extend lines. Place tangency points T at both places.

8. Repeat now from C, same opening. Place points T1

9. Finally center at O1, and join the tangency points from that side, repeat the procedure from O2 to close the figure.

OVAL KNOWING THE MAYOR AXIS.

1. We draw a horizontal line AB of 9cm, and divide it in three equal parts. Place O1 and O2

2. Using O1 and O2 as centers, draw two circumferences with the radius equal to the third part of AB. (from O1 to A)

3. The places where the circumferences intersect to each other will be point O3 and O4.

4. Using a ruler, draw lines from O3 to O1 and O2 and extend. Repeat from O4.

5. The intersection from that lines and the circumferences will be the tangency point T.

6. Using the compass, center at O3 and with an opening from O3 to tangency point 1 draw a large arc from each opposite tangency point.

7. Repeat from O4.8. Finally re-draw the arcs using O1 and O2 as

centers in order to close the figure.

OVOIDIt is a closed and flat curve composed of two arcs of circumference of equal radius, and two other of different radius, one of them is a semicircumference. It has an axis of symmetry that contains the two centers of unequal arcs.

OVOID KNOWING THE MINOR AXIS.

1. We draw a horizontal line AB of 6cm.2. Find the perpendicular bisector for AB,

extend the line and place point O at the middle point.

3. Using the compass, center at O and draw a circumference with a radius from O to A.

4. Place point CD where the circumference and the vertical line intersect.

5. With the ruler, draw lines from A and B to point D, extend the lines beyond that point.

6. Center at A, set the opening from A to B and draw a large arc until the extended line. Place tangency point T1.

7. Repeat the procedure from B, same opening. Place point T2.

8. Using D as center join both tangency points. 9. Finally re-draw the semicircumference using

O as center in order to close the figure.

OVOID KNOWING THE MAYOR AXIS.

1. We draw a vertical line AB of 9cm.2. Divide the AB line in six equal parts. 9/63. Using the second division from the top as

center, set the opening from 2 to B and draw a large arc.

4. On the second division from the top, using perpendicular bisector process draw a perpendicular line to AB, extend the line so it will intersect the recently drawn large arc. Place point E and F.

5. Using the same division as center, set the opening from 2 to A and draw a semicircumference place point C and D.

6. With a ruler draw a line from E and F to the fifth division on AB (point 5) and extend the lines.

7. Center at F, set the opening from F to C, draw a large arc from C to the extended line, place tangency point T1.

8. Center at E, set the opening from E to D, draw a large arc from D to the extended line, place tangency point T2.

9. Using point 5 as center join the two tangency points.

10. Finally re-draw step 5 in order to close the figure.

AESTHETIC EDUCATION10TH GRADE: Q2P3 (Part1)

Drawing Tools to be used:

Compass, pencil, ruler, set squares, protractor, eraser, markers and a properly framed A4 cardboard.

LINES AND DIMENSIONING

LINES Lines is one important aspect of technical drawing. Lines are always used to construct meaningful drawings. Various types of lines are used to construct drawing, each line used in some specific sense.

Lines are drawn following standard conventions mentioned in BIS (SP46:2003). A line may be curved, straight, continuous, segmented. It may be drawn as thin or thick. A few basic types of lines widely used in drawings are shown below.

Table 1. Types of Lines used in Technical Drawing.

CONVENTIONS USED IN LINES

International systems of units (SI) – which is based on the meter.

Millimeter (mm) - The common SI unit of measure on engineering drawing.

Individual identification of linear units is not required if all dimensions on a drawing are in the same unit (mm).

The drawing should contain a note: ALL DIMENSIONS ARE IN MM.

Typical figures showing various lines used in the construction of engineering drawing is shown below.

A typical use of various lines in an engineering drawing is shown in figure below:

DIMENSIONING

The size and other details of the object essential for its construction and function, using lines, numerals, symbols, notes, etc are required to be indicated in a drawing by proper dimensioning. These dimensions indicated should be those that are essential for the production, inspection and functioning of the object and should be mistaken

as those that are required to make the drawing of an object. The dimensions are written either above the dimension lines or inserted at the middle by breaking the dimension lines.

Normally two types of dimensioning system exist. i.e. Aligned system and the unidirectional system.

In the aligned system the dimensions are placed perpendicular to the dimension line in such a way that it may be read from bottom edge or right hand edge of the drawing sheet. The horizontal and inclined dimension can be read from the botto whereas all the vertical dimensions can be read from the right hand side of the drawing sheet. In the unidirectional system, the dimensions are so oriented such that they can be read from the bottom of the drawing.

The aligned system and unidirectional system of dimensioning.

RULES TO BE FOLLOWED FOR DIMENSIONING.

Each feature is dimensioned and positioned only once.

Each feature is dimensioned and positioned where its shape shows.

Size dimensions – give the size of the component.

Every solid has three dimensions, each of the geometric shapes making up the object must have its height, width, and depth indicated in the dimensioning.

Typical dimension lines

  DIMENSIONING CONSISTS OF THE FOLLOWING:

A thin, solid line that shows the extent and direction of a dimension. Dimension lines are broken for insertion of the dimension numbers

Should be placed at least 10 mm away from the outline and all

other parallel dimensions should be at least 6 mm apart, or more, if space permits

The important elements of dimensioning consists of extension lines, leader line, arrows and dimensions.

Extension line A thin, solid line perpendicular to a dimension line, indicating which feature is associated with the dimension. There should be a visible gap of 1.5 mm between the feature’s corners and the end of the extension line.

Leader line A thin, solid line used to indicate the feature with which a dimension, note, or symbol is associated. Generally this is a straight line drawn at an angle that is neither horizontal nor vertical. Leader line is terminated with an arrow touching the part or detail. On the end opposite the arrow, the leader line will have a short, horizontal shoulder. Text is extended from this shoulder such that the text height is centered with the shoulder line

Arrows 3 mm wide and should be 1/3rd as wide as they are long - symbols placed at the end of dimension lines to show the limits of the dimension. Arrows are uniform in size and style, regardless of the size of the drawing.

Various types of arrows used for dimensioning

THE SPECIFICATION OF DIMENSION LINES

Dimensioning of angles: The normal convention for dimensioning of angles are illustrated in figure below.

AESTHETIC EDUCATION10TH GRADE: Q2P3 (Part2)

BASIC PROJECTION DRAWING

Confronted with the task of communicating the design, development and structures of machines to manufacturers and builders. The shape and size of various parts of a machine and its structure must be recorded on plane sheets in a systematic way for communication.

The pictorial view of the object does not carry all the details, especially the inner details and correct shape of complicated parts. Different methods, therefore, are implied for describing the exact shape based on the ‘projectors’ drawn.

PRINCIPLE OF PROJECTION

If straight lines are drawn from various points on the contour of an object to meet a plane, the object is said to be projected on that plane. The figure formed by joining, in correct sequence, the points at which these lines meet the plane, is called the projection of the object. The lines from the object to the plane are called projectors.

TYPES OF PROJECTIONS

The projections are classified according to the method of taking the projection on the plane. A classification of most common projection is shown below:

OBLIQUE PROJECTION

Oblique projection is a method of drawing objects in 3 dimensions. It is quite a simple technique compared to isometric or even perspective drawing. However, to draw accurately in oblique projection traditional drawing equipment is needed.

Straight 30cm ruler Set Square (30º and 45º rulers)

DEFINITION OF AN OBLIQUE PROJECTION

A way of drawing which a three-dimensional object is represented by a drawing in which the face, usually parallel to the picture plane, is represented in accurate or exact proportion, and all other faces are shown at any convenient angle other than 90° typically 45, 30 or 60°.

ANGLES OF PROJECTIONS IN OBLIQUE

In oblique drawings, the three axes of projection are vertical, horizontal, and receding. The front view (vertical & horizontal axis) is parallel to the frontal plane and the other two faces are oblique (receding).

THE DIRECTION OF PROJECTION

The direction of projection can be top-left, top-right, bottom-left, or bottom-right. The receding axis is typically drawn at 60, 45, or 30 degrees

DIMENSIONING OBLIQUE DRAWINGS

All dimension lines, extension lines, and arrowheads must lie in the planes of the object to which they apply. It is up to you if you choose to use aligned or unidirectional dimensioning

DIFFERENCE: CAVALIER VS CABINETwww.youtube.com/watch?v=Vy8CBG1ztrw

There are two types of Oblique Projection Drawings, CAVALIER AND CABINET.

In Cavalier Oblique Drawings, all lines (including receding lines) are made to their true length. This means that if the object shown on the right is 30mm deep, you would draw it 30 mm deep.

In Cabinet Oblique Drawings, receding lines are shortened by typically one-half their true length to compensate for distortion and more closely represent what the human eye would see. This means that if the object shown on the right is 30 mm deep, you would draw it 15 mm deep.

Cabinet oblique drawings are the most used form of oblique drawings.

MOST COMMON ANGLES AND SCALES

Type of Oblique

Oblique Projection Angle(α)

Receding Axis Scale

Cavalier30º 145º 160º 1

Cabinet

30º 2/345º 1/260º 3/2

Arctan(2) = 63.43º Special 1/2

AESTHETIC EDUCATION10TH GRADE: Q2P3 (Part3)

ORTHOGRAPHIC PROJECTION

WHAT IS ORTHOGRAPHIC PROJECTION?

We need to ask ourselves what is Orthographic Projection? Basically it is a way a representing a 3D object on a piece of paper. This means we make the object become 2D. The difference between Orthographic Projection and any other drawing method is that we use several 2D views of the object instead of a single view.

Is a method of representing a three dimensional object in two dimensions.

The word orthographic means straight description. The straight description here stands for the parallel projectors from the object to infinity.

Orthographic Projection is a way of drawing a 3D object from different directions. Usually a front, side and plan (top) view are drawn so that a person looking at the drawing can see all the important sides. Orthographic drawings are useful especially when a design has been developed to a stage whereby it is almost ready to manufacture.

The planes are mutually perpendicular to each other and are known as ‘Principal Planes’ of projectors, named Horizontal Plane (HP), Vertical Plane (VP) and Profile Plane (PP).

GL: Ground line, divides the HP and the VP.

Orthographic Projection gives us a very clear method of communicating ideas and objects. It is a method that every engineer in the world recognizes. Because of this we can reproduce any object drawn orthographically. This is very important.

Think of how many languages there are in the world... imagine how much of a problem this presents to designers and manufacturers across the world. Imagine an engineer in Germany who wants a plastic bottle manufactured in Japan. How do you think he will overcome the language barrier? The easiest way is to use a drawing. However drawing can be interpreted differently by different people. A good example is shown below. Is the blue face on the inside or outside of the box?

All of these problems can be overcome using Orthographic Projection. An engineer in Germany can have a plastic bottle made in Japan, exactly as he wants it, without any problem if he sends an Orthographic drawing of the bottle. This makes Orthographic Projection a Universal language among people in engineering professions!