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

Question

Problem 4 The Scotch Yoke is a mechanism that transforms circular motion of a -rank (2) into reciprocating motion of a slider (shaft 4). The motion is considered to be harmonic, as it is a petitive. The acceleration of point A is defined by a -1.8 sin kt, where a is m/s? 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 02 (NOTE: all points on slider 4 have same velocity and acceleration, since it is rectilinear motion)

Explanation / Answer

a=-1.8 sinkt

v=1.8k coskt (integrate accelaration,a)

v=0.6 when t=0

then 0.6=1.8 k cos 0

k=1/3

v=1.8 * 1/3 * cos t/3 =0.6 cos t/3

displacement, s = v t

s=0.6 t cos t/3

find s and v when t=0.5 sec

velocity , v = 0.6 cos (0.5/3)=0.6 m/sec

displacement , s = 0.6 * 0.5 * cos (0.5/3) = 0.3 m

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