Question

?Y2 ?Y3 AY1 A 04 B 06 X2 777 02 d Y2? Y3 AY1 C ?2 B e a, b, c, d, e ARE LINK LENGTHS a) For the slider crank mechanism shown, using the vector diagram and the vector loop method prove that angle $\theta_2$ expressed as a function of the link lengths and the distance of joint B from origin $O_6$ is: Your proof must include the following steps: i. Develop governing vector equations for the loop(s). ii. Express vectors in their compact complex form. iii. Separate vector equations into real and imaginary terms. iv. Combine the two resulting simultaneous equations to develop your expression for $\theta_2$. b) Using the expression derived in part (a), develop expressions for $\theta_{21}$ and $\theta_{22}$. Illustrate the difference between the two angles with sketches of the linkage. c) Reproduce the table at right, exactly as shown and then complete the table (using d as the independent variable), using the following lengths and your derived expressions: b=75mm, c=200mm, e=300mm. Show at least one sample calculation. d (mm) $\theta_{21}$ (degrees) $\theta_{22}$ (degrees) 25 50 75 100 125 150 175

          ?Y2
?Y3
AY1
A
04
B
06
X2
777
02
d
Y2?
Y3
AY1
C
?2
B
e
a, b, c, d, e ARE LINK LENGTHS
a) For the slider crank mechanism shown, using the vector
diagram and the vector loop method prove that angle $\theta_2$
expressed as a function of the link lengths and the distance of
joint B from origin $O_6$ is:
Your proof must include the following steps:
i. Develop governing vector equations for the loop(s).
ii. Express vectors in their compact complex form.
iii. Separate vector equations into real and imaginary terms.
iv. Combine the two resulting simultaneous equations to develop
your expression for $\theta_2$.
b) Using the expression derived in part (a), develop expressions
for $\theta_{21}$ and $\theta_{22}$. Illustrate the difference between the two angles
with sketches of the linkage.
c) Reproduce the table at right, exactly as shown and then
complete the table (using d as the independent variable),
using the following lengths and your derived expressions:
b=75mm, c=200mm, e=300mm. Show at least one sample
calculation.
d (mm) $\theta_{21}$ (degrees) $\theta_{22}$ (degrees)
25
50
75
100
125
150
175

?Y2
?Y3
AY1
A
04
B
06
X2
777
02
d
Y2?
Y3
AY1
C
?2
B
e
a, b, c, d, e ARE LINK LENGTHS
a) For the slider crank mechanism shown, using the vector
diagram and the vector loop method prove that angle θ2
expressed as a function of the link lengths and the distance of
joint B from origin O6 is:
Your proof must include the following steps:
i. Develop governing vector equations for the loop(s).
ii. Express vectors in their compact complex form.
iii. Separate vector equations into real and imaginary terms.
iv. Combine the two resulting simultaneous equations to develop
your expression for θ2.
b) Using the expression derived in part (a), develop expressions
for θ21 and θ22. Illustrate the difference between the two angles
with sketches of the linkage.
c) Reproduce the table at right, exactly as shown and then
complete the table (using d as the independent variable),
using the following lengths and your derived expressions:
b=75mm, c=200mm, e=300mm. Show at least one sample
calculation.
d (mm) θ21 (degrees) θ22 (degrees)
25
50
75
100
125
150
175

Added by Victoria V.

Question

Please give Ace some feedback