THEORY OF MACHINES AND MECHANISNMS I LAB MANUALEXPERIMENT NO. 2 TITLE : RADIUS OF GYRATION BY BIFILAR SUSPENSION METHOD
To determine the radius of gyration of given bar using bifilar suspensionmethod.
Uniform steel bar, cylindrical weights, stop watch.
Fig 1 shows the general arrangement for carrying out experiment. A
uniform rectangular section bar is suspended from support frame by twoparallel cords.
Two small chucks fitted in the frame and other endssecured in bifilar bar. Ends of these cords pass through a chuck so as tofacilitate for change in length of the cord it is possible to adjust length of chord by loosening the chuck.The suspension may also be used to determine radius of gyrationof any body,In this case the body under investigation is bolted to thecenter. Radius of gyration of combined bar and body is then determined.
1) Suspend the bar from chuck and adjust length of chord ' L' convenientlynote the suspension length of each cord must be same.2) Allow the bar to oscillate about the vertical axis passing through center of gravity and measure periodic time 'T' by knowing time for 20
oscillations.3) Repeat the experiment by mounting the weights one equal distancefrom the center.
Consider bar AB whose moment of inertia is to be determine issuspended by two parallel strings as shown in figure 2.Let, L = length of each string.m = mass of bar.K = radius of gyration about the vertical axis through G.I = mass moment of inertia about the vertical axis through G.
2r = distance between two stringsT = tension in each string
= angle of twist of bar.
= angle of twist of string
= angular accelaration of the bar.Initial position of bar is AGB. Now, if bar is set gently in vibration inhorizontal plane, it will start oscillating about vertical axis through its masscenter G. when bar is twisted about its C.G, through an angle
, bar is inposition A'GB' as shown. When bar is getting
as angular displacement,then string is getting
as angular displacement about vertical, distancemoved by point A is arc AA'
arc AA' = r
( 1)PIMPRI CHINCHWAD COLLEGE OF ENGG. MECHANICAL ENGG DEPT