Problem 4 The Scotch Yoke is a mechanism that transforms circular motion of a cr

Question

Problem 4 The Scotch Yoke is a mechanism that transforms circular motion of a crank (2) into reciprocating motion of a slider (shaft 4). The motion is considered to be harmonic, as it is repetitive. The acceleration of point A is defined by a=-1.8 sin kt, where a is m/s2 and t is sec. Also, k-3 rad/sec. If the initial conditions are x-0 at time t-0, and v-0.6 m/s at t-0, find the velocity and displacement of point A when t-0.5 sec. Let the origin be at Qe (NOTE: all points on slider 4 have same velocity and acceleration, since it is rectilinear motion) O.

Explanation / Answer

Acceleration, a = -1.8 sin(kt)

If v , represent instantaneous velocity then

a = dv/dt = -1.8sin(kt).........(1)

Integrating (1)

v = (1.8cos(kt)/k) + C

Where C is constant of integration

at t= 0 , v = 0.6

Then , 0.6 = 0.6 +C

C =0

Therefore ,v = (1.8 cos(kt))/k ..........(2)

If x represent instantaneous position then

v= dx/dt

Integrating (2)

X = (1.8 sin(kt)/k^2) + C1 where C1 is constant of integration

At t=0, X=0

Therefore,

X = (1.8 sin(kt))/k^2

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