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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 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°

Limitation of Sine Bar

 • Sine bars are not used beyond 45 degree 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

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