Angular Measurement
• No absolute standard is required for angular measurement.
• Units of measurement – Degrees (°): defined as 1/360 of a circl
e – Radians (rad): defined as 1/(2π) of a circle
. • 1 radian = 57.29578°
Common Instruments Used:
• Protractors
• Sine Bars & Sine Centers
• Angle Gauges
• Spirit Level
• Autocollimator
• Angle Dekkor
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 = 1degree 24 div of VS = 46 div on MS or 1/12th of 23
LC of bevel protractor = 2- (23/12) = 1/12
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’
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
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
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)
Sine Centers
• Useful for testing of conical work up to 60°.
• Centers ensure correct alignment of the work piece.
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.
Angle Gauge
s 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
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