Reference no: EM13343071
Linkage analysis: The mechanism shown below is used to obtain a linear and an angular output. Its dimensions are OA =1.7 in, AB = 3 in, BC = 2.5 iv, OC = 3.2 in, AD= 1 in, DE= 5 in, e =4 in. Assume the angular velocity of the input crank (link OAD) is constant at ω = 500 rpm.
a) Calculate the mobility of the linkage.
b) Use the constraint equation for the distance between points A and B to solve for ψ as a function of θ. Use the loop equation for point B to solve for the coupler angle cp as a function of θ and ψ. Compute the limits of the input angle θ.
c) Use the constraint equation between points D and E to solve for the slide s as a function of θ. Use the loop equation for point E to solve for the second coupler angle δ, θ as a fimction of θ and s. Compute the new limits of the input angle θ from the quadratic equation vn s.
d) Use Maple to plot the values of the slide s and the output angle w as a function of the input angle θ going from θmin to θmax (If there is no limit for θ, then plot for θ between θ and 2Π radians.)
e) Compute the coordinates of the midpoint of the couple DE. Use Maple to plot the coupler curve for this point as a function of the input angle θ
f) Compute the velocity of point E, the input(θ)/output(ψ) angular velocity ratio and the input/slide velocity ratio. Plot the output angular velocity and the slide velocity as a fimction of θ using Maple.
g) Extra Credit: Use Maple to create a simulation of the movement of the linage for values of θ going from θmin to θmax
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