o The size of the object in accepted in unit is known as dimension.
o The allowable variations for each dimension is known as tolerance.
o Visible lines :
It is a continuous thick line which represent features that can be seen in the current view.
o Hidden lines :
It is a dash thick line which represent features that cannot be seen in the current view.
o Centre line :
It is chain thin line which represent symmetry, centre of circles.
o Dimension and Extension line :
It is continuous thin line which represent the size and location of features on drawing.
o Phantom line :
A line drawn by alternating a long dash, followed by two short dashes.
o Projection line (construction line):Lines that are light thin which are drawn perpendicular to the plane of projection and parallel to each other.Scale of any drawing shows relativity to the actual size of any object.
Scale are denoted as a:b
o If
any object is drawn such that a >b, then it is known as enlarging scale.
i.e. drawing size greater than actual size.
Eg.
5 : 1, 3 : 1, 10 : 1, etc.
o If
any object is drawn such that a<b, then it is known as reducing scale. i.e. .
drawing size smaller than actual size.
Eg.
1 : 10, 1 : 100, 1 : 200, etc.
o If
any object is drawn such that a=b, then it is known as full size scale. i.e. .
drawing size actual size of object are equal. Here a=b=1 (always). i.e. 1 : 1.
o Representation
factor (scale) =
Length
of drawing (a)
Actual
length of object (b)
o Unless
mentioned specific, the unit of length dimension is always in milimeters (mm).
o A
straight line is one dimension geometry.
o Size
of circle can be shown as Radial dimension or Diametral dimension.
o R25
represents size of circular part. This indicates a circle of radius 25 (mm
unless mentioned).
o
20 represents size of circular part in
terms of diameter. This indicates a circle of diameter 20 mm.
o A
point in engineering drawing is dimensionless quantity.
o Among
T, F, Y and M, M is more stable letter.
o In
inclined lettering, the letters are inclined through 70-75 degree to
horizontal.
GEOMETRIC FEATURES
Angle
o Two lines when share
same end point from an angle.
o The intersecting point
of two line is vertex of angle.
o If ‘θ’ is angle then,
a. 0°<θ<90° - acute angle
b. 90°<θ<180°-obtuse angle
c. θ = 90°-Right angle
d. θ = 180°-Straight
angle/Straight line
e. 180°<θ<360°-Reflex angle
f. θ=360°-Whole angle
o If θ1 and θ2 are two angles then
a. If θ1+θ2 = 90°, then θ1and θ2 are known as
complementary angle to each other.
b. If θ1+θ2 = 180°,then θ1 and θ2 are known as
supplementary angle to each other.
c. If θ1+θ2 = 360°,then θ1and θ2 are known as
explementary or conjugate angle to each other.
o Two lines are said to
be orthogonal or perpendicular if angle between them is 90° (π/2).
o Angles that have same
measure (i.e. same magnitude) are said to be congruent.
o Two angles opposite
each other, formed by two intersecting straight lines that form an “X” shape
are called vertical angles or opposite angles which are equal to each
other.
o Angle that share a
common vertex and a common side but do not share any interior points are adjacent
angles.
o The measures of the
interior angle of a simple polygon with n sides add up to (n-2)⨉180°.
Eg. Sum of interior
angles of triangle = (3-2)⨉180°= 180°.
Sum of interior angles
of quadrilateral = (4-2)⨉180°= 360°
Note: To find one interior
angle of such polygon sum of interior angle must be divided by side of polygon.
o One full turn means
360°.
o Angle between two plane
is dihedral angle which is acute angle between two lines normal to the planes .
o The angle between plane
and an intersecting line =90°-‘Ɵ’
intersection of line and
plane.
Polygon
o Polygon
is a 2-D plane figure that is bounded by a closed path or circuit.
o Name
of polygon and their edges
o Decagon
- 10,
o Hendecagon
- 11,
o Dodecagon
– 12,
o Tridecagon
– 13,……………………….
o Icosagan
– 20.
o Note:-Exterior
angle at each vertex can be found by subtracting interior angle from 360°.
Triangle
o A
geometrical polygen with 3 sides and 3 vertices.
o A
triangle in which all sides are equal (all interior angle are 60°) is
equilateral triangle.
o A
triangle in which all sides are equal is known as Isosceles triangle.
o A
triangle in which all sides (all angles) are different is scalene triangle.
o A
right triangle (right-angled triangle or rectangular triangle) has one of its
interior angle 90°. It follows pythagorerean theorem.
o Trianle
that do not have an angle that measures 90° are called oblique triangles.
o A
triangle that has all interior angles measuring less than 90° is an acute
triangle or acute angled triangle.
o A
triangle that has one angle that measures more than 90° is an obtuse triangle
or obtuse angled triangle.
o In
a triangle ABC, a+b > c (always valid),known as triangle inequality.
o For
similar triangles :
a. AA (Angle – Angle)
F
If two corresponding internal angles of
two triangles have same measure.
b. SSA (Side-Side, Angle)
F If
two corresponding sides are in proportion and their included angles have same
measure.
c. SSS (Side-Side-Side)
F If
three corresponding sides of two triangles are in proportion.
o
For congurent triangles:
a. SAS (Side-Angle-Single):
F
If two side and their included angle is
same of measure.
b. ASA
(Angle-Side-Angle):
F If
two angle and their included side is same of measure.
c. SSS
(Side-Side-Side):
F If
corresponding sides are equal.
d. AAS (Angle-Angle-Side):
F If
two angle and a corresponding (non-included) side is equal.
e. HL (hypotenuse-leg):
F Two
right angled triangle are congurent if their hypotenuse and legsure of same
measure.
Square
o It
is a regular quadrilateral with all side equal equal and all interior angle
equals to 90°.
o A
figures which is both rectangle and rhombus is square.
o If
a circle is circumscribed around square area of circle = 1.57 ⨉ area
of square.
o If
a circle is inscribed inside square area of circle = 0.79 ⨉
area of square.
o If
a circle is inscribed inside square.
o Ratio
of diagonal (across corner length) of square to a side (across flat length) of
square is √2 : 1.
Quadrilateral
o Four
sided polygon.
o Rhombus
or rhomb is a type of parallelogram in which all sides are equal, opposite
sides are parallel and opposite angles and equals.
o Rhomboid
is a type of parallelogram in which adjacent sides are of unequal lengths and
angle are oblique.
o Oblong
is a term which denotes rectangle that is not a square.
o Trapezium
is a quadrilatrial in which two opposite sides are parallel .
o Cyclic
quadrilateral is the one in which all Four vertices lie on a circumscribed
circle.
o Tangential
quadrilateral is the one in which all four edges are tangent to an inscribed
circle.
o Bicentric
quadrilateral is the one which is both cyclic and tangential.
Points, lines and circles associated with
triangles
o Orthocentre:
Intersection of the altitudes of triangle.
o Incentre:
Intersection of angle bisector of triangle. (It is also centre
of circle inscribed in a triangle).
o Circumcentre:
Intersection of perpendicular bisector of all sides of
triangle.(It is also centre of circumscribing circle).
o Centroid:
Intersection of medians.
o Altitude
of triangle: Line through one vertex which is
perpendicular to the opposite side to the vertex.
o Medians
of triangle: Line through one vertex which meets the
midpoints of opposite side to the vertex.
o Straight
line through centroid, orthocentre, circumcentre and centre of nine point
circle is Euler’s line.
o If
a circle is outscribed by an even side regular polygon (the circle is inside
and the polygon is outside) then diameter is equal to the across flat (A/F)
length of regular polygon.
o If
a circle is inscribed by an even side regular polygon (the circle is outside
and the polygon is inside) then diameter is equal to Across corner (A/C)
length of the regular polygon.
o Maximum
tangents that can be drawn from outside point on a circle is 2.
o If
a circle is inscribed and circumscribed by squares then area of bigger square
is double than area of small square.
o If
two circle one inscribed and another circumscribed by same square then area of
bigger circle is double than area of small circle.
Conic Section
o When
a cone is cut by a section plane.
a. Perpendicular to axis of cone, conic
section → circle.
b. Making an angle with axis greater than
the generator, conic section → ellipse.
c. Parallel to one of generators, conic
section → hyperbola.
d. When a section plane cuts both the parts
of double cone on side of axis, conic section →
hyperbola.
Note: In
this case if section plane cuts the cone parallel to axis, conic section →
rectangular hyperbola.
o Conic
section based on eccentricity (e)
i.
If e > 1, hyperbola.
ii.
If e < 1, ellipse.
iii.
If e = 1, parabola
Curves
o Involute:
It is path of a point on a straight line which rolls without slip along
circumference of cylinder. It is 2D geometry.
o Archemedian
spiral: It is locus of a point which moves around
a centre at uniform angular velocity and at the same time moves moves away from
the centre at uniform linear velocity. It is 2D geomatry.
o Right
hand cylindrical Helix and Right hand conical Helix
Helix:
F
It is a curve generated on the surface of
the cylinder by a point which revolves uniformly around the cylinder and at the
same time either up or down its surface.
F
Helix angle on a cylinder having pitch P
and diameter D is equal to tan¯ˡ(P/πD).
F
It is 3-dimensional geometry.
F
If cylinder is replaced by cone on above
definition then it will be right hand conical helix.
F
Top view of conical helix is spiral and
cylinder helix is circle.
o Cycloid:
The locus of point on circumference of a cylinder which rolls
without slip along at flat surface. It is 2-dimension locus.
Solids
o Tetrahedron:
Four triangular faces, four corners, triangular base pyramid.
o Hexahedron(cube):
Six square face, 8 corners, special square prism.
o Octahedron:
Eight faces, six corners.
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