765 linear acceleration of the saw blade 25mm crank at 45 de

7-65 linear acceleration of the saw blade

25mm crank at 45 degrees and 300 rpm

y and the Ulldt acceleration of link 4. 65. Figure P7.65 illustrates the driving mechanism in a saber saw. At the instant shown, the crank is rotat ing at a constant rate of 300 rpm clockwise. Graphically determine the linear acceleration of the saw blade. 25 mm Crank 450 Saw blade FIGURE P7.65 Problems 65, 66, and 72. in Figure P7.65, the

Solution

solution:

1)given mechanism is similar to slider crank mechanism as in this case saw blade is behaving as slider

2as at instant angle m=45

crank length=r=25 mm

connecting rod length=l=x-25sin45/sin45

where piston position to be x

here loop closure equation is

xe^i270=re^i315+le^i225

on putting value real part become

xcos270=25cos315+((x-25sin45)/sin45)cos225

x=35.3553 mm

hence=l=25 mm from above relation

4)here obliquity ratio=n=l/r=25/25=1

5)hence linear accelaration of saw blade as piston is

As=x\'\'=rw^2(cosm+(cos2m/n))

at m=45 degree

w=2*pi*300/60=10pi=31.415 rad/s

As=x\'\'=25*31.415^2*(cos45+cos90/1)

as=x\'\'=17446.13 mm/s^2=17.446 m/s^2