Figure below shows an offset slider crank mechanism. The size and location data

Question

Figure below shows an offset slider crank mechanism. The size and location data are: r_2 = 3", r_3 = 8", r_4 = 2", theta_2 = 70degree, and theta_1 = 20degree. The auxiliary equation is theta_4 = theta_1-90degree. Force F is opposite to R_1 and passes through point C. Its magnitude is 100 lb (F = 100 lb). Perform position analysis and report the solution corresponding to the figure shown. Perform kineto-static analysis and report all joint forces/moment (there are three pin joints and one slider joint) as well as torque T_2 that balances force F for the position shown.

Explanation / Answer

Position Analysis:

Position Analysis: The vector loop equation is written as

r2 i2 e + r3 3 i e r4 i4 e = 0.

Since 4 = 0, then

r2 i2 e + r3 3 i e r4 = 0

or r2(cos2 + isin2) + r3(cos3 + isin3) r4 = 0

Collecting real and imaginary parts yield

Real: r2cos2 + r3cos3 r4 = 0

Imag: r2sin2 + r3sin3 = 0

The problem of the position analysis is defined as Given: r2, r3 and 2 Find: 3, r4

Using imaginar part

r2sin2 + r3sin3 = 0

   sin3 = 3 sin70 / 8

           = -0.35

3 = arc-0.35

   = -20.480

    

      

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