Rr411405 Advanced Kinematics Dynamics of Machines

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Code No: RR411405 Set No. 1

4. A f our -link RGGR crank-rocker mechanism shown in figure 3. The knowns arethe position and plane of rotation of the input link, the plane of rotation of theoutput link, and dimensions of all four links. Find the positions of all moving linkswhen the input crank is set to θ2 = −450 as shown below. Solve the problem usinggraphical approach. Given data: O2.A = 2 cm, AB=7 cm, O4.B = 8 cm. [16]

Figure 3:

5. Determine the couple on crank ‘2’ to be applied for equilibrium of the system, whena force of 500 N acts on the connecting rod at point ‘C’ as shown in figure 4. also

determine the resultant of forces exerted on its frame. [16]

Given data: O2.A = 15 cm, A.B = 45 cm, A.C = 12 cm

6. Define Energy contribution coefficient. Describe the Quinn’s Energy distributionmethod for the direct determination of input velocity of the mechanism at anyinstant.

[16]

7. State the ‘two position synthesis of a four-bar mechanism’. Give the step by stepprocedure to obtain the synthesized four-bar crank-rocker and slider crank mecha-nisms by using two position synthesis. [16]

8. Synthesize a four-bar linkage that will, in one of its positions, satisfy the followingvalues for the angular velocities and angular accelerations. [16]

ω2 = 20 rad/s ; α2 = 0rad/s

ω3 = 8 rad/s ; α3 = 100 rad/s

ω4 = 10 rad/s ; α4 = −150 rad/s

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Figure 4:

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IV B.Tech I Semester Supplementary Examinations, February 2007ADVANCED KINEMATICS & DYNAMICS OF MACHINES

(Mechatronics)Time: 3 hours Max Marks: 80

Answer any FIVE Questions

All Questions carry equal marks⋆ ⋆ ⋆ ⋆ ⋆

1. (a) State kutz batch criterion for determining mobility of a Spatial mechanism.

(b) Find the mobility of the selected planar mechanisms. (figure 1) [6+10]

Figure 1:

2. (a) Write about complex mechanisms and give example.

(b) Write the applications of Goodman’s method to the analysis of low and highcomplexity mechanisms.

(c) Write about sign conventions of Goodman’s approach. [5+6+5]

3. (a) What is cognate linkages.

(b) Write about inflection circle & inflection points. [8+8]

4. A four -link RGGR crank-rocker mechanism shown below. The knowns are the

position and plane of rotation of the input link, the plane of rotation of the outputlink, and dimensions of all four links. Find the positions of all moving links whenthe input crank is set to θ2 = 600 as shown in figure 2. Solve the problem usingAnalytical approach.

Given data: O2.A = 4 cm, AB = 15 cm, O4.B = 10 cm. [16]

5. The driving moment applied on link ‘2’ is shown in figure 3. Determine the force

on link ‘4’ that is necessary to be applied for equilibrium of the linkage. Alsodetermine the state of loading on the connecting rod.

Given data: O2.A = 10 cm, A.B = 32 cm. [16]

6. Explain Equivalent-mass-and force method in Dynamic motion analysis, for thedetermination of input acceleration of the mechanism at any instant. [16]

7. What is the difference between two position synthesis and three position synthesisof four-bar mechanism, give step by step procedure to obtain the synthesized four-bar crank-rocker mechanism by using pole technique. [16]

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Figure 2:

Figure 3:

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1. (a) What is meant by mobility of a mechanism?

(b) Find the mobility of the selected planer mechanisms. (figure1) [4+12]

Figure 1:


(b) Write the applications of Goodman’s method to the analysis of low and high

complexity mechanisms.(c) Write about sign conventions of Goodman’s approach. [5+6+5]

3. Find the fixed end coordinates of cognate four-bar mechanism, use the followingdata. OA. OB = 100 mm, OA.A = 50 mm, OB.B = 90 mm, AB = 66 mm, α =400, AC = 30 mm, assume input link inclination (θ) = 300. (figure 2) [16]

4. Using Hartman’s procedure constract the inflection circle for a moving plane shownbelow. Assume ωm = 0.5 rad/s (c.c.w), Os → S = 7 cm, P → S = 3 cm, θs = 300

(figure 3)

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Figure 2:

Figure 3:

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5. The driving moment applied on link ‘2’ is shown in figure 4. Determine the forceon link ‘4’ that is necessary to be applied for equilibrium of the linkage. Alsodetermine the state of loading on the connecting rod.

Given data: O2.A = 10 cm, A.B = 32 cm. [16]

Figure 4:

6. The following are particulars of the slider crank mechanism shown in figure 5. O2.A= 6 cm, AB = 18 cm, AG3 = 9 cm, φ f = 450 The weight of link ‘2’ (W 2 ) = 6 N ,W 3 = 10 N, W 4 = 5 N, The mass moment of Inertias I 02 = 0.15 N-cm2, I G3 = 0.75N-cm2, T 2=60 N-cm (cw) constant, F4 decrease uniformly from 25 N in phase-I to20 N in phase-II, directed to the left. Calculate its velocity and acceleration of theinput link

[16]

Figure 5:

7. (a) Write about chebyshev spacing of precision points

(b) What is dwell mechanism? Explain it clearly.

(c) What are the errors in function generation synthesis problems? [5+6+5]


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ω2 = 20 rad/s ; α2 = 0rad/s

ω3 = 8 rad/s ; α3 = 100 rad/s

ω4 = 10 rad/s ; α4 = −150 rad/s

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1. (a) State kutz batch criterion for determining mobility of a planar mechanism.

(b) Find the mobility of the selected mechanisms. (figure1) [6+10]

Figure 1:


(b) Write the applications of Goodman’s method to the analysis of low and highcomplexity mechanisms.

(c) Write about sign conventions of Goodman’s approach. [5+6+5]

3. Find the fixed end coordinates of cognate four-bar mechanism, use the followingdata. OA. OB = 100 mm, OA.A = 50 mm, OB.B = 90 mm, AB = 66 mm, α =400, AC = 30 mm, assume input link inclination (θ) = 300. (figure 2) [16]

4. Using Hartman’s procedure construct the inflection circle for link ‘3’ shown in figure3. Assume ω3 = 0.5 rad/s, AB = 5 cm. [16]

5. The driving moment applied on link ‘2’ is shown in figure 4. Determine the forceon link ‘4’ that is necessary to be applied for equilibrium of the linkage. Also

determine the state of loading on the connecting rod.Given data: O2.A = 10 cm, A.B = 32 cm. [16]

6. Explain Equivalent-mass-and force method in Dynamic motion analysis, for thedetermination of input acceleration of the mechanism at any instant. [16]

7. (a) Write about chebyshev spacing of precision points

(b) What is dwell mechanism? Explain it clearly.

(c) What are the errors in function generation synthesis problems? [5+6+5]

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Figure 2:

Figure 3:

Figure 4:

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ω2 = 20 rad/s ; α2 = 0rad/s

ω3 = 8 rad/s ; α3 = 100 rad/s

ω4 = 10 rad/s ; α4 = −150 rad/s

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Rr411405 Advanced Kinematics Dynamics of Machines

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