To draw curved lines, as shown in fig. 24. At the word _one_, point; at
the word _two_, point three inches directly above; _three_, at the same
distance above again make a point; now draw a curve as shown, joining
the middle point and the upper point; now draw the curve as shown below
it; finally complete figure as shown.
[Illustration: Fig. 26.]
[Illustration: Fig. 27.]
[Illustration: Fig. 28.]
[Illustration: Fig. 29.]
[Illustration: Fig. 30.]
Figs. 25 to 30 are to be practiced, making first the points and then
connecting them by the curves to complete the figures.
When two or more students are working together, with each having a
blackboard, the counting may be in concert--or a teacher could count for
a class. In these line examples care should be used in making them of
uniform length. There is a difference to be noted between a crooked line
and a broken line, the latter being a straight line and the former
deviating from it.
Square chalk crayons are the best for hand work, as lines of an even or
uniform width can be drawn with them.
A very fine effect is produced by using two thicknesses of chalk, one
being double the thickness of the other; the heavy lines being used on
the shade side of objects will produce a good effect, giving thickness
and body to the object.
Round chalk crayons are used in the compasses to draw circles, but hand
lines drawn with them are not so neat as those produced with the
square-shaped chalk.
To obliterate or remove the construction, or false lines made on the
blackboard, a wooden handle two inches in diameter with a cone end 3 or
4 inches long, covered with chamois skin or soft cloth tightly wrapped
round the cone and fastened with a tack or drawing pin, makes the best
implement to erase lines not required, the point of the cone will remove
these without destroying the lines or curves which meet them.
Sponges, chamois skin or cloth rubbers are used to rub out the chalk
drawings and clean the blackboard.
The best height for a diagram on the blackboard is not higher than the
head, nor lower than the elbow.
Horizontal lines should be made from the left to the right; the body and
arm being moved with the hand, and kept in the same relative position
with it, will steady the hand.
Curved lines to the left should be drawn first, enabling the eye to take
in not only the curve in process of formation but that already made.
Passing the crayon in the hand, over the intended curve previous to
marking it, will guide the eye and give confidence to the hand in
chalking the curve.
A proper distance from the blackboard is essential, the face being about
two feet away from it.
Draw with the whole arm extended from the shoulder-joint, not from the
elbow or wrist.
[Illustration: Fig. 31.]
[Illustration: “There are more ways than one of telling things: by
speech, by writing, by printing, also by pictures and drawings.”
Knowles]
[Illustration: TERMS DEFINITIONS]
[Illustration: ELECTRA.]
Preliminary Terms and Definitions.
Like all the arts, drawing has a nomenclature of its own, and nothing
can be more helpful to the beginner than to know the name of things
relating to the art of drawing. This is a language almost peculiar to
itself, and used daily and hourly by many thousands of superintendents,
foremen and master mechanics, as well as by owners, designers and
draughtsmen, hence its introduction at this early stage.
=ALTITUDE.=--This is the elevation of an object above its base, or the
perpendicular distance between the top and bottom of a figure.
[Illustration: Fig. 33.]
[Illustration: Fig. 34.]
[Illustration: Fig. 35.]
[Illustration: Fig. 36.]
[Illustration: Fig. 37.]
=ANGLE= is the difference in the direction of two lines which meet or
tend to meet. The lines are called _the sides_ and the point of
meeting, the _vertex_ of the lines.
To make an angle apparent, the two lines must meet in a point, as _A
B_ and _A C_, which meet in the point _A_, as shown in fig. 33.
Angles are measured by degrees.
A _Degree_ is one of the three hundred and sixty equal parts of the
space about a point in a plane.
Angles are distinguished in respect to magnitude by the terms Right,
Acute and Obtuse Angles.
A _Right Angle_ is that formed by one line meeting another, so as to
make equal angles with that other.
The lines forming a right angle are _perpendicular to each other_.
An _Acute Angle_ is less than a right angle. See Fig. 35.
An _Obtuse Angle_ is greater than a right angle. See Fig. 36.
Obtuse and acute angles are also called _oblique angles_; and lines
which are neither parallel nor perpendicular to each other are called
_oblique lines_.
The _Vertex_ or _Apex_ of an angle is the point in which the including
lines meet.
An angle is commonly designated by a letter at its vertex; but when
two or more angles have their vertices at the same point, they cannot
be thus distinguished.
For example, when the three lines _A B_, _A C_, and _A D_ in fig. 37
meet in the common point _A_, we designate either of the angles
formed, by three letters, placing that at the vertex between those at
the opposite extremities of the including lines. Thus, we say, the
angle _B A C_, etc.
=APEX.=--The summit or highest point of an object.
=ARC.=--See circle.
=AXIS OF A SOLID.=--An imaginary straight line passing through its
center.
=AXIS OF A FIGURE.=--A straight line passing through the center of a
figure, and dividing it into two equal parts.
=BASE.=--The base of a solid figure is that on which it stands--the
lowest part.
=BISECT.=--To divide into two equal parts.
=BISECTOR.=--A line which bisects.
[Illustration: Fig. 38.]
=CIRCLE.=--A _Circle_ is a plane figure bounded by one uniformly
curved line, all of the points in which are at the same distance from
a certain point within, called the _Center_.
The _Circumference_ of a circle is the curved line that bounds it.
The _Diameter_ of a circle is a line passing through its center, and
terminating at both ends in the circumference, as _A C B_.
The _Radius_ of a circle is a line extending from its center to any
point in the circumference. It is one-half of the diameter. All the
diameters of a circle are equal, as are also all the radii _C D_, _C
B_ and _C A_.
An _Arc_ of a circle is any portion of the circumference, as _B D_ and
_A D_.
_Semi-Circle._--Half a circle formed by bisecting it with a diameter,
as _A C B_. Fig. 38.
An angle having its vertex at the center of a circle is measured by
the arc intercepted by its sides. Thus, the arc _A D_ measures the
angle _A C D_, and in general, to compare different angles, we have
but to compare the arcs, included by their sides, of the equal circles
having their centers at the vertices of the angles.
=CIRCUMSCRIBE.=--To draw a line of figures about or outside, such as a
circle drawn around a square touching its corners or angles.
_Inscribe._--To draw a line or figure inside or on the interior, such
as a circle drawn within a square touching its sides.
=CONCAVE.=--Curving inwardly.
=CONE.=--A solid body or figure having a circle for its base, and its
top terminated in a point or vertex.
=CONSTRUCTION.=--The making of any object.
=CONTOUR.=--The outline of the general appearance of an object.
=CONVERGENCE.=--Lines extending towards a common point.
=CONVEX.=--Rising or swelling into a round form--the opposite to
concave.
=CORNER.=--The point of meeting of the edges of a solid, or the two
sides of a plane figure.
=CROSS-HATCHES.=--In free-hand drawing the use of lines crossing each
other to produce light and shade effects.
=CURVE.=--A line of which no part is straight.
_Reversed Curve._--One whose curvature is first in one direction and
then in the opposite direction.
_Spiral Curve._--A plain curve which winds about and recedes,
according to some law, from its point of beginning, which is called
its center.
=CYLINDER.=--A solid bounded by a curved surface and by two opposite
faces called bases; the bases may be any curved figures and give the
name to the cylinder; thus a circular cylinder is one whose bases are
circles.
=CYLINDRICAL.=--Having the general form of a cylinder.
=DEGREE.=--The 360th part of a circle.
=DESCRIBE.=--To make or draw a curved line; to draw a plan.
=DESIGN.=--Any arrangement or combination to produce desired results
in industry or art. To delineate a form or figure by drawing the
outline--a sketch.
=DEVELOP.=--To unroll or lay out.
=DIAGONAL.=--A right line drawn from angle to angle of a quadrilateral
or many angled figure and dividing it into two parts.
=DIAMETER.=--A right line passing through the center of a circle or
other round figure terminated by the curve and dividing the figure
symmetrically into two equal parts.
=EDGE.=--The intersection of any two surfaces.
=ELEVATION.=--The term elevation, vertical projection and _front
view_--applied to drawings--all have the same meaning.
=FACE.=--One of the plane surfaces of a solid; it may be bounded by
straight or curved edges.
=FINISHING.=--Completing a drawing whose lines have been determined by
erasing unnecessary lines and strengthening and accentuating where
this is needed.
=FORESHORTENING.=--Apparent decrease in length, owing to objects being
viewed obliquely; thus a wheel, when seen obliquely, instead of
appearing round, presents the appearance of an ellipse.
=FREE-HAND.=--Executed by the hand unaided by instruments.
=GENERATED.=--Produced by.
=GEOMETRIC.=--According to geometry.
=HALF-TINT.=--The shading produced by means of parallel equidistant
lines.
=HEMISPHERE.=--Half a sphere obtained by bisecting a sphere by a
plane.
=HORIZONTAL.=--Parallel to the surface of smooth water. In drawing, a
line drawn parallel to the top and bottom of the sheet is called
horizontal.
=INSCRIBE.=--See circumscribe--its opposite.
=INSTRUMENTAL.=--By the use of instruments.
=LINE.=--A line has length, only, as A C; a right line is a straight
line, the shortest line that can be drawn between two points, A----C.
_Straight._ One which has the same direction throughout its entire
length.
_Curved._ One no part of which is straight.
_Broken._ One composed of different successive straight lines.
_Mixed._ One of straight and curved lines.
_Center._ A line used to indicate the center of an object.
_Construction._ A working line used to obtain required lines.
_Dotted._ A line composed of short dashes. - - - - - -
_Dash._ A line composed of long dashes. -- -- --
_Dot_ and _Dash_. A line composed of dots and dashes alternating. -- ·
-- · --
_Dimension._ A line upon which a dimension is placed.
_Full._ An unbroken line, usually representing a visible edge. ------
_Shadow._ A line about twice as wide as the ordinary full line.
A straight line is often called simply a line, and a curved line a
curve.
=LONGITUDINAL.=--In the direction of the length of an object.
=MODEL.=--A form used for study.
=OBLIQUE.=--Neither horizontal nor vertical.
=OBLONG.=--A rectangle with unequal sides.
=OVAL.=--A plane figure resembling the longitudinal section of an egg;
or elliptical in shape.
=OVERALL.=--The entire length.
=PARALLEL.=--Having the same direction and everywhere equally distant.
=PATTERN.=--That which is used as a guide or copy in making things.
_Flat._ One made of paper or other thin material.
_Solid._ One which reproduces the form and size of the object to be
made.
=PERIMETER.=--The boundary of a closed plane figure.
=PERPENDICULAR.=--At an angle of 90°.
=PERSPECTIVE.=--View; drawing objects as they appear to the eye from
any given distance and situation, real or imaginary.
=PLAN.=--Plan, horizontal projection and _top view_ have the same
meaning.
=PLANE FIGURE.=--A part of a plane surface bounded by straight or
curved lines, or by both combined.
[Illustration: Fig. 39.]
=POLYGON.=--A plane figure bounded by straight lines called the sides
of the polygon. The least number of sides that can bound a polygon is
three. Polygons bounded by a greater number of sides than four are
denominated only by the number of sides.
A polygon of five sides is called a _Pentagon_; of six, a _Hexagon_;
of seven, a _Heptagon_; of eight, an _Octagon_; of nine, a _Nonagon_,
etc.
_Diagonals_ of a polygon are lines joining the vertices of angles not
adjacent.
The _Perimeter_ of a polygon is its boundary considered as a whole.
The _Base_ of a polygon is the side upon which the polygon is supposed
to stand.
The _Altitude_ of a polygon is the perpendicular distance between the
base and a side or angle opposite the base.
[Illustration: Fig. 40.]
A _Quadrilateral_ is a polygon having four sides and four angles.
A _Parallelogram_ is a quadrilateral which has its opposite sides
parallel.
The side upon which a parallelogram stands and the opposite side are
called respectively its lower and upper bases.
A _Rectangle_ is a parallelogram having its angles right angles.
A _Square_ is an equilateral rectangle, fig. 41.
[Illustration: Fig. 41.]
[Illustration: Fig. 42.]
[Illustration: Fig. 43.]
[Illustration: Fig. 44.]
[Illustration: Fig. 45.-49.]
A _Rhomboid_ is an oblique-angled parallelogram.
A _Rhombus_ is an equilateral rhomboid, fig. 42.
A _Trapezium_ is a quadrilateral having no two sides parallel, fig.
43.
A _Trapezoid_ is a quadrilateral in which two opposite sides are
parallel, and the other two oblique, fig. 44.
=A POLYHEDRON= is a solid bounded by planes. There are five regular
solids which are shown in figs. 45, 46, 47, 48 and 49. A regular solid
is bounded by similar and regular plane figures.
Fig. 45.--The _tetrahedron_, bounded by four equilateral triangles.
Fig. 46.--The _hexahedron_, or cube, bounded by six squares.
Fig. 47.--The _octahedron_, bounded by eight equilateral triangles.
Fig. 48.--The _dodecahedron_, bounded by twelve pentagons.
Fig. 49.--The _icosahedron_, bounded by twenty equilateral triangles.
=PRISM.=--A solid whose bases or ends are very similar plane figures,
and whose sides are parallelograms; prisms are called triangular,
square, etc., according as the bases are triangles, squares, etc.
=PRODUCE.=--To continue or extend.
=PROFILE.=--An outline or contour.
=PROJECTION.=--The view of an object obtained upon a plane by
projecting lines perpendicular to the plane.
=QUADRANT.=--The fourth part; a quarter; the quarter of a circle.
=QUADRISECT.=--To divide into four equal parts.
=SECTION.=--A projection upon a plane parallel to a cutting plane
which intersects any object. The section generally represents the part
behind the cutting plane, and represents the cut surfaces by diagonal
lines.
=SECTIONAL.=--Showing the section made by a plane.
=SHADOW.=--Shade and shadow have about the same meaning.
=SOLID.=--A solid has three dimensions--length, breadth and thickness.
=SPHERE.=--A solid bounded by a curved surface every point of which is
equally distant from a point within called the center.
=SURFACE.=--The boundary of a solid. It has but two dimensions--length
and breadth. Surfaces are plane or curved.
A _Plane Surface_ is one upon which a straight line can be drawn in
any direction.
A _Curved Surface_ is one no part of which is plane.
The surface of the sphere is curved in every direction, while the
curved surfaces of the cylinder and cone are straight in one
direction.
The surface of a solid is no part of the solid, but is simply the
boundary of the solid. It has two dimensions only, and any number of
surfaces put together will give no thickness.
[Illustration: Fig. 50.]
[Illustration: Fig. 51.]
[Illustration: Fig. 52.]
[Illustration: Fig. 53.]
[Illustration: Fig. 54.]
=SYMMETRY.=--_Design._ A proper adjustment or adaptation of parts to
one another and to the whole.
=TRISECT.=--To divide into three equal parts.
=TRIANGLE.=--A triangle is a polygon having three sides and three
angles. _Tri_ is a Latin prefix signifying three; hence a Triangle is
literally a figure containing three angles.
A _Scalene Triangle_ is one in which no two sides are equal. See fig.
50.
An _Isosceles Triangle_ is one in which two of the sides are equal.
See fig. 51.
An _Equilateral Triangle_ is one in which the three sides are equal.
An _Equiangular Triangle_ is one having its three angles equal. An
_Acute-Angled Triangle_ is one in which each angle is acute.
A _Right-Angled Triangle_ is one which has one of the angles a right
angle. See fig. 53.
An _Obtuse-Angled Triangle_ is one having an obtuse angle. Fig. 54.
Equiangular triangles are also equal sided, and vice versa.
=VERTICAL.=--Upright or perpendicular. Vertical and perpendicular are
not synonymous terms.
=VERTEX.=--See Angle, Quadrilateral, Triangle. The vertex of a solid
is the point in which its axis intersects the lateral surface.
=VIEW.=--See Elevation. Views are called front, top, right or left
side, back, or bottom, according as they are made on the different
planes of projection. They are also sometimes named according to the
part of the object shown, as edge view, end view, or face view.
=WORKING DRAWING.=--One which gives all the information necessary to
enable the workman to construct the object.
[Illustration]
[Illustration: FREEHAND DRAWING]
[Illustration: Fig. 55.]
Free-Hand Drawing.
A free-hand drawing is executed with the unaided hand and eye, without
guiding instruments or other artificial help. It is necessary to be
known that all drawing required cannot possibly be done by rule and
compass, but that some portions must be drawn “free-hand,” trusting to
the eye alone.
Hence, it is important that the student should be able to sketch at
sight from objects he may see, or to draw roughly, with a piece of chalk
or a pencil, pieces of mechanism required to be represented.
Practice in free-hand should go along with mechanical drawing as
progress is made, and thus cultivating both branches equally.
“A simple sketch will often,” as has been rather roughly said, “express
more than yards of talk.”
Even a slight sketch refreshes the memory, and in the case of the
preparation of a complete set of drawings, with a view to the making of
a thoroughly finished mechanical drawing, the proper course to pursue
is, to make a general sketch, letter the various parts for reference,
and then prepare a series of detailed sketches, similarly lettered, and
diffuse with dimensions.
Everyone, whatever his specialty, feels to-day that the ability to
sketch rapidly and clearly is among the absolute necessities for correct
and prompt transactions of business, in giving and executing orders and
doing business with persons outside his profession.
Mistakes and misunderstandings may be averted by means of rough sketches
taken at the time and shown for confirmation; this also saves assistants
from getting into trouble, especially if they pin the sketch to the
order, for reference, in case of the arising of any dispute. These are a
few of the advantages of knowing how to sketch quickly and correctly.
In “free-hand” any sort of pencil is better than none, but there is a
considerable advantage in having a good serviceable article--a pencil
not too soft nor too hard, and one which will retain its point for some
little time.
Fig. 55 shows the approved position in which the pencil should be held
while sketching. The pencil should be held firmly between the thumb and
first finger of the right hand; press the second finger against the
pencil at the opposite side to the thumb pressure, so that the pencil is
firmly held by the contact of the thumb and two fingers--the third and
fourth fingers just coming into easy reach of the paper surface--the
wrist or ball of the hand resting lightly on the surface of the
work--the arm resting on the desk or drawing-board for steadiness.
The motion of the pencil is produced from the movement of the fingers
and thumb, principally in the vertical strokes, and the horizontal
strokes are produced by fingers and thumb, combined with a wrist or
elbow motion; the oblique lines and curves are produced with a free
movement, with nothing cramped or confined about the finger joints.