MIME 3300 Homework 4 11/7/2017 ______Due: 11/14/2017

Please write you final answer on this page and submit it together with the detailed calculations.

1. 1) Using the algebraic approach we studied in the class, design a slider-crank linkage to have a stroke of 600 mm and a time ratio, Q, of 1.20. The design must satisfy the following constraints:

. The length of the connecting arm, r3 must be equal to three times the length of the crank, r2. This will ensure that the slider acceleration is lower than a maximum allowable value. . Packaging requirements dictate that the length of the crank must be less or equal to 300 mm and the length of the connecting arm is less or equal to 1200 mm. Also the vertical distance of the center of rotation of the crank from the plane of the slider must be less than 500 mm.

Calculate r2, r3, e and angles  and , corresponding to the working and the return strokes, respectively.

2) Draw the slider-crank mechanism you found in problem 1 at the positions in which the mechanism is folded and fully extended. Select an appropriate scaling factor so that the drawing fits in a page.

3) Using a graphical approach, draw a four-bar linkage for which the throw angle, , is 800 and the imbalance angle is 200. Select a rocker length of 40 mm.

4) Design a four-bar linkage to support the seat in the extended position and fold to the closed position shown below. The mechanism should fit in the space shown. Specify the lengths of the four links. Draw the mechanism in the extended and folded position and in an intermediate position. Note that the seat surface shown should be able to slide on one of the links of the mechanism, which is horizontal at the extended position. Seat surface (when mechanism is in extended position)

300 mm

300 Link of mechanism mm at extended position 500 mm

Seat surface (folded) 500 mm Hint for problem 4:

One solution is to use a four bar linkage with the vertical wall being the ground link (link 1) and the rocker supporting the seat surface (link 4). In the extended position, the mechanism will look like this:

Seating surface (link 4)

B O4

Link 3 A Wall (link 1)

Link 2

O2

To fold the mechanism, push joint A up and to the right. In the folded position, all links are collinear. In order to determine the length of the four links, write the equations that these lengths must satisfy in the folded and extended positions. For example, in the extended position, the following equation is satisfied:

(O4O2)2  (BO4)2  (O2B)2

Then select the link lengths to satisfy all the requirements.