Slider Crank Mechanism - Engineering Assignment Help

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Question #11

The simple mechanism below is to be used on a manufacturing line. The crank AB is pow- ered by a motor at A and its constant clockwise rotational motion, !AB, results in back and forth horizontal motion of the block at C. The block is on a smooth surface which can be assumed frictionless. Before this mechanism can be used, a force analysis must be performed in order to estimate the stresses in the individual components. The client is particularly concerned about the link, BC, and therefore needs the forces at B and C. The length of the crankshaft is R and the length of link BC is L. The material properties of BC are such that the center of mass is located at point D, located a distance d from B. The mass of link BC is mD, the mass of the block is mC, and link BC has a mass moment of inertia of ID.

1. Draw a free-body diagram for (a) the link BC, and (b) the block C. Neglect the e↵ect of the weight of the link BC and the weight of the block at C.
2. Write the force and momentum balances for the block and the link.
3. To solve the above equations, you will need to perform some kinematic analysis. You should have five (5) unknown kinematic variables (accelerations) from Step 2 above.
Derive expressions for all five variables in terms of the crank angle, ? (i.e. there should be no other angle in your expression).2
4. Using your set of equations from Step 2, construct a matrix equation of the form Ax = b, where x is a column vector with the unknown forces, A is a coecient matrix, and b is a column vector containing the remaining known quantities. At this point, please do not substitute your kinematic expressions from Step 3.
5. Let !AB = 60 rpm, R = 0.0485m, L = 0.141m, d = 0.0364m, mD = 4 kg, ID = 0.005 kg · m2, mC = 4 kg. Plot the force components at B and C as a function of the crank angle, ?, for one full rotation. You will need to solve your matrix equation to do this.

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