crankshaft angle, calculus help. It\'s not obvious to me. I think I\'m having is

Question

crankshaft angle, calculus help. It's not obvious to me. I think I'm having issues with the visualization here.

Consider the mechanical device illustrated. The crank OA (driving link) revolves counterclockwise about the fixed point O at five revolutions per second. The length OA is r = 20 cm. The driven link AC of length 85 cm is a slotted arm constrained by the fixed pin B at a distance a = 60 cm from O. At any given instant, let the angle of rotation AOB be denoted by theta, the corresponding angle ABO be denoted by alpha and the distance AB be denoted by x. Assume the angle theta = 0 at time t = 0. Briefly explain why it is obvious that the maximum value of XC occurs when t = 0, whereas the minimum value occurs at t = 0.1. Hence, what are the right-most and left-most coordinates of C?

Explanation / Answer

The Distance XC will become Least when the AO and AC Become in one Line , Because we know that Straight Disiatnce is Least

Now the AO and AC will become in one Line when theta = 0 degree

And we are given theta = 0 when t = 0

So Minimum Xc at t = 0

======================================

The Distance Xc will be Maximum when the Link OA in the Opposite Direction to the Link AC

This will Happen when theta = 180 degree

Now we have given

w = 5rev/sec

Therefoe

In 1sec angle rotated = 5*360 = 1800 degree

So For 180 degree Time required = (1/1800)*180

= 1/10 = 0.1 sec

So Maximum at Xc = 0.1 sec

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