In the mechanism shown, block B is fixed and has a profile described by the foll

Question

                    In the mechanism shown, block B is fixed and has a profile described by the following relation:                 

                    y = h[ 1 + 1/2(x/d)^2 - 1/4(x/d)^4 ]                 

                    The follower moves with the shuttle A, and the tip C of the follower remains in contact with B.

                    Assume that h = 6mm., d = 22mm, and A is made to move from x= -d to d=d with a constant speed v0 = 0.3 m/s. Determine the ACCELERATION of C for x = 14mm. Express your answer im m/s^2.

In the mechanism shown, block B is fixed and has a profile described by the following relation: y = h[ 1 + 1/2(x/d)^2 - 1/4(x/d)^4 ] The follower moves with the shuttle A, and the tip C of the follower remains in contact with B. Assume that h = 6mm., d = 22mm, and A is made to move from x= -d to d=d with a constant speed v0 = 0.3 m/s. Determine the ACCELERATION of C for x = 14mm.

Explanation / Answer

y = h[ 1 + 1/2(x/d)^2 - 1/4(x/d)^4 ]

dy/dt = h[x*v0/d^2 -x^3*v0/d^4]

d2y/dt2 = h[v0*v0/d^2 - 3x^2*v0*v0/d^4]

acc of C = h[v0*v0/d^2 - 3x^2*v0*v0/d^4] =

or, acc of C = 0.006*[(0.3*0.3)/(0.022^2) - 3*0.014^2*0.3*0.3/(0.022^4)] = -0.23973 m/s^2

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