1. Angular Measurement
• No absolute standard is required for angular
measurement.
• Units of measurement
– Degrees (°): defined as 1/360 of a circle
– Radians (rad): defined as 1/(2π) of a circle.
• 1 radian = 57.29578°
3. Universal Bevel Protractor
• Construction: It consists of
– Main scale is graduated in degrees
& rotates with the rotation of the
adjustable blade.
– Vernier scale is divided into twelve
equal parts on each side of zero.
– Acute angle attachment
• Accuracy: Upto 5 minutes.
Least count on Main scale = 10
24 div of VS = 46 div on MS
or 1/12th of 230
LC of bevel protractor
= 2- (23/12) = 1/12
4. Optical Bevel Protractor
• It has a glass circle fitted
inside the main body
• Glass circle is divided into
10’ throughout its 3600.
• Provision for
magnification is available.
• By approximation, it may
read upto 2’.
5. Sine Bars
• Hardened and precision ground tools used for:
– Measuring known angles or locating any work to a
given angle.
– Checking of unknown angles.
• Used in conjunction with slip gauges and dial
indicator.
• Depending on the accuracy they may be
– Grade A: 0.01 mm/m of length
– Grade B: 0.02 mm/m of length
6. Sine Bar: Construction
• Made of high carbon, high chromium corrosion resistant
steel hardened ground and stabilized
• Two accurately lapped rollers of the same diameter are
located a fixed distance apart.
• Surface of sine bar is parallel to the center lines of the
plug/rollers.
• Sine bars sizes: of 100, 200,
250, 300 mm
• Holes are drilled in the body
for easy handling and
reduced weight
7. Sine Bar: Principle
• If sine bar is the
hypotenuse of right
angled triangle and h
the height of slip
gauges as shown in
Figure
h = Height in mm
L = Center distance in mm
Sinθ = Opp / Hyp = (h/ L)
10. Sine Bar Error
• Accuracy of an angle set by a sine bar depends on:
– Error in spacing of roller centers (dL)
– error in or errors in combination of slip gauges (dh)
• The height of slip gauge combination (h) required to
set angle (ϴ) is given by:
h = L sin ϴ
Partial differentiation of the above equation yields:
dh/dϴ = (sin ϴ) (dL /dϴ) + L cos ϴ
or dh = (sin ϴ) dL + (L cos ϴ) dϴ
or dϴ = tan ϴ ((dh/h) - (dL /L))
• As the angle increases, the error (dϴ) in the angular
measurement increases. Above 45 °, the graph for dϴ
vs. ϴ rises sharply, so a sine bar is never used beyond
45°.
11. Limitation of Sine Bar
• Sine bars are not used beyond 450 because:
– It is difficult to handle & position on slip gauges.
– Large angular error may result due to slight error
in length.
– Long gauge stacks are not as accurate as short
ones
– Different deformation is observed at the two
rollers because at large angles, weight load gets
shifted towards the fulcrum roller
12. Sine Centers
• Useful for testing of
conical work up to 60°.
• Centers ensure correct
alignment of the work
piece.
13. Sine Plate
• Allow angles to be
measured and set in
each of two orthogonal
planes.
• A work piece is secured
to the top plate and the
bottom plate is secured
to a machine tool table
using clamps or a
magnetic chuck.
14.
15. Sine Bar: Advantages& Disadvantages
Advantages
• Used for accurate &
precise angular
measurement.
• It is cheap.
Disadvantages
• Application is limited for
a fixed center distance
between two plugs or
rollers.
• It is fairly reliable till
about 150. But
inaccuracies increase
with increase in angles.
16. Angle Gauges
Wedge shaped block used as standards for
angle measurement.
Large number of combinations by adding or
subtracting gauges are possible
Nominal angles of combination angle gauges
Degrees 1 3 9 27 41
Minutes 1 3 9 27
Seconds 3 6 18 30
• Square block is also available
18. Spirit Level
• Used for measuring small angle or inclinations and also enable the
position of a surface to be determined with respect to the horizontal.
• It consists of a sealed glass tube that is:
– Nearly filled with ether & contains a bubble of ether vapors
– Ground on its inside surface to a convex form with a large radius of
curvature R
– A scale is engraved on the glass at the top of the tube.
• The glass tube is set in the base and adjusted in such a way that when
the base is horizontal the bubble rests at the center of the scale which is
engraved on the glass.
19. Spirit Level
• Principle: When the base of the level
is moved out of the horizontal, the
bubble moves along the scale. Thus,
l = Rα = Rh/L
(For small values of α)
• Thus sensitivity of the level increases
as
– Radius of curvature (R)increases
– Length of the base (L) decreases
• Scale division values:
– For precise measurements: 4 to 10
– For ordinary purposes: 10 to 40
• Very sensitive to variation in
surroundings temperature
20. Types of Spirit Level (Contd.)
According to BS 1958, three types of spirit levels are recommended.
• Type 1.:
– It has an unrelieved flat base of steel, hardened and lapped.
– The base length of spirit level varies between 100 to 200 mm.
– Effective length of the level can be varied by wringing two gauge
blocks on the base at the desired distance apart.
• Type 2
– It is mounted in cast iron or steel body, having a base formed with
feet bearing surfaces at the two ends (middle portion being
relieved).
– Base length 250-500 mm
– The bearing surface may be plain or contain a longitudinal 120° V-
groove for use on cylindrical surfaces.
• Type 3:
– It is a square block level about 200 mm square and made of cast
iron.
– The four bearing surfaces are flat and may have the middle portion
relieved. Alternatively, the base and one adjacent-surface may
contain a longitudinal 120° vee groove for use on cylindrical
surfaces in which case a short cross-level is provided.
22. Clinometer
• A special case of the application of
spirit level.
• Uses:
– Checking angular faces, and relief
angles on large cutting tools and milling
cutter inserts.
– For setting inclinable table on jig boring;
machines and angular work on grinding
machines etc.
• In some clinometers, a graduated
circle is supported on accurate ball
bearings such that when released, it
always takes up the position relative
to the true vertical. The reading is
taken against the circle to an
accuracy of 1 second with the aid of
Vernier.
• Reading up-to 1′ is possible
24. Autocollimator
An optical instrument used for the
measurement of small angular differences.
It is essentially an infinity telescope and a
collimator combined into one instrument.
25. Principle
• When light from a point source
(placed at the principal focus) passes
through a collimating lens, it emerges
as a parallel beam of light.
• If this beam strikes a plane reflector
normal to the optical axis, it will be
reflected back along its own path and
focussed at the same point O.
• However, if the reflector is tilted by
an angle θ, then the reflected rays
makes an angle 2*θ and converges at
point O’.
OO’ = (2* θ)*(f)
where f is focal length
26.
27. Autocollimator (Cond.)
• Sensitivity and angular measuring range
depend on focal length and the effective
aperture.
• A large separation might cause the reflected
rays to completely miss the lens and no image
will be formed.
28. • A cross line target graticule is positioned at the focal plane of telescope
objective.
• Rays of light reach the objective via beam splitter and are projected from
objective as parallel.
• A proportion of the returned light passes straight through the beam
splitter and the return image of the target crossline is therefore visible
through the eyepiece.
• The linear displacement of the graticule image is measured by an
eyepiece graticule , optical micrometer or electronic detector system ,
scaled directly in angular units.
29. • Visual Autocollimator
– Reflected image of a pinhole light source gives the displacement.
– Resolution: 3-5” over a distance of 1.5m
• Digital Autocollimator
– An electronic photo-detector detects the reflected light.
– Output may be transferred to a data acquisition system
– Resolution up-to 0.01 arc-second
• Laser Auto-collimator
– Ideal for measuring angles of small objects (1mm diameter)
– Long measuring range (15m or more)
– Better accuracy
– Can be used for non- mirror finish surface.
30. • Measurement of straightness and flatness.
• Precise angular indexing in conjuction with
polygons.
• Comparative measurement using master
angles.
• Assessment of squareness and parallelism of
components.
• Measurement of small linear dimensions.
31. Angle Dekkor
• Used as a comparator
• Working
– Image of an illuminated scale in the focal
plane of the collimating lens is projected as a
parallel beam by the collimating lens after
striking a reflector.
– In the field of view of microscope, another
datum scale is fixed across the center of
screen.
– Changes in angular position of the reflector in
two planes are indicated by changes in the
point of intersection of the two scales.
• Accuracy: up-to 1’.
• It is used in combination with angle
gauges to.
– Measure angle of a component
– For precise angular setting for machining
operations.
– Checking the sloping angle of a V-block
