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Question: 4supl in the mechanisms shown in the figure 1 the...

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4-Supl. In the mechanisms shown in the figure: 1) The black link is input and the orange link is output. 2) Aslider moves along the orange link. 3) The slider is pin-joined with the black link at point A. 4) O, and O2 are fixed by pin joints Ra RI Questions a) Using the analytical (vector loop) method, solve b in terms of a, c, and e b) Express cos(6) and sin(6) in terms of a, c, and 6;, Assume a = 1 and c Use tools such as MATLAB to plot the variation of 63 when the input link makes a full revolution (ie. when 6, changes from 0° to 360°). c) Based on your plot in (b), can the output link make full revolution? d)lf your answer to (c) IS NO, can you use the result in (a) to MATHEMATICALLY determine the values of when the output link is at its two extreme positions (ie. when 63 is at its max and min)? Compare the solution to your plot in (c). Based on the results, draw the mechanism when the output link is at its two extreme positions, respectively. e) Redo (b) and (c) assuming a 2 and c 1 Steps to Question (a) 1) Form the loop of vectors equation for this linkage (using vector and angle definitions shown above) 2) Simplify the equation and break it down into two scalar equations. 3) Solve cos() and sin(e) in terms of , a, b, and c. 4) Use cos(6)sin(e)1 to eliminate 6. Then solve b in terms of e, a, and c 5) Plug the solution of b back into the expressions of cos(63) and sin(63). You will end up with solutions of cos(6) and sin(6) in terms of a, c. and Steps to Question (b) 1) Define a vector for e,, starting from 0 and ending with 360 with a step size of1 In MATLAB: theta2 0 : 0·01 : 2 *pi = 2) For each solve using the function atan2 in MATLAB or the equivalent function in a different tool. atan2 (sine, You can add 360 when the angle is negative to make the solution in 0-360 cosine) gives a unique solution of the angle (-180 - 180).Hints to Question (c): For example, below are plots ofG3 versus θ2 in two example cases. In both, e2 varies from 0 to 360. E5 400 In this case, the output link can only rotate between 135 degree and 225 degree. In this case, the output link can make full revolution. Hints to Question (d): From (a) you get tan(0) in terms of a, c, and e. Use a-1 and cv2 to simplify the expression of tan(3). When 6 is at max or min, can solve e d tan0 0. From this equation you

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