How many degrees of freedom does the planar joint shown

Question

Question 1. Select the best answer out of given choices:

1. How many degrees of freedom does the planar Joint shown have?

a. 1
C. 3
d. 4

2. A planar mechanism with four links, three pin joints and one sliding Joint is called
a. Grashof
b. Structure
c. Slider-crank.
d. isomer

3. A link that has a pin joint with ground and is able to make a full rotation is called is called
a. Crank
b. Slider
c. Rocker
d. Cam

4. Which is the correct direction of velocity of point A on the rotating link shown?

a.
b.
c.
d.

5. Which is the correct direction of normal acceleration of point A on the rotating link shown?
a.
b.
c.
d.

6. If R is the pitch radius of a gear and z is its number of teeth, then the module of the gear is given by:
a. 2R/z
b. R/2z
c. z/2R
d. 2z/R

7. In the gear train shown, which gear is an idler gear?

a. 3
b. 4
c. 5
d. 6

8. A mechanism with four links, three revolute (pin) joints and one prismatic (sliding) joint is called:
a. Grashof mechanism
b. Slider-Crank Mechanism
c. Planer mechanism
d. isomer

9. If we replace a revolute joint by a slider joint in a planar Mechanism, its degree of freedom will _____provided that at least two revolute joints remain in the loop
a. Increase by one
b. Decrease by one
c. Remain the same
d. Increase by two
e.

10. The six bar isomer shown in the figure is a

a. Stephen's six bar isomer
b. Watt's six bar Isomer
c. Gruebler's Six bar Isomer
d. None of the Above

Question 2. A Determine the number of links (L), the number of joints (3) and the degrees of freedom, m, of the 5 cylinder radial engine shown below (left) with its schem (right).

 

Question 3.

Q1 Choose the best answer out of given choices
1. The number of nodes in a ternary link are
a. 5
b. 2
c. 1
d. 3

2. A __ is pivoted to the ground and has oscillatory motion.
a. Rocker
b. Ground
c. Crank
d. Coupler

3. The simplest joint is the combination of two links and has order
a. Zero
b. One
c. Two
d. None of the above

4. The number of inputs that need to be provided in order to create a predictable output is called
a. DOE'
b. Order of the mechanism
c. Both (a) and (b)
d. None of the above

5. Identify the following as a Higher Pair or Lower Pair

a. Higher Pair
b. Lower Pair
c. Both (a) and (b)
d. None of the above

6. Any unconnected link in a plane has
a. 0 DOF
b. 2DOF
c. 3 DOF
d. 6 DOF

7. What is the DOF of the following structure?

a. 1
b. 0
c. 2
d. 3

Question 4: In the slider-crank mechanism shown,

R₂ = 100 mm, R₃ = 400 mm, θ₂ = 45 θ3 = 10.2^o and Vs = 150 mm/s to the right

Find (a) the distance OB, and (b) the angular velocities ω₂ and ω₃.

Question 5: For the offset slider-crank mechanism shown in figure below, link 2 is 20 mm in length, link 3 is 50 mm, angle θ2 is 45o and the offset OA is 10 mm. Find θ2 the angle of link 3 with x axis and slider position OC.

(a) Determine the number of links, the number of joints and the degree of freedom, m of the planar mechanism shown below.

(b) A four-bar linkage has the following dimension: Ground= 90mm, Crank = 30 mm, couple = 500mm, follower = 60 mm. Check if this is a Grashof(Class I kinematic Chain) or non- Grashof linkage.

Question 6: Using the given plot of torque T vs crank angle θ of an engine over two revolutions

(a) Calculate the total energy input, U, of the engine over this angle range and then mean torque Tm. (Don't forget to change the angle into radians)

(b) If the mean speed of the engine is 100 rad/s and the coefficient of speed fluctuation is Cs = 0.10, calculate the mass moment of inertia of the flywheel. Also determine the maximum and minimum and maximum speeds.

Question 7:

In the planetary gear train shown, the sun gear 2 has 40 teeth and the internal ring gear 4 has 801 teeth. Gear 2 rotaters counter-clockwise at ω2 = 150 rad/s, while gear 7 is held stationary.

a) Calculate the number of teeth of gear 3 = 20
b) Calculate the speed and direction of rotation of the arm.

Question 8: The unbalanced rotating system shown has

m₁ = 10 g, m₂ = 20 g, R₁ = 100 mm, R₂ = 50 mm.

Find two masses, m₃ and m₄, that should be placed in planes 3 and 4 respectively, at radius 20 mm each, in order to balance the system.

Question 9: In the double slider mechanism shown.

ψ = 20^o and ψ = 30^o and V_s = 20 mm/s to the right

Find (a) the distance OA (b) the angular velocity ω_AB

Question 10: The unbalanced rorating system shon has

m_B = 5 kg at R_B = 75 mm. Θ_B = 90^o and m_C = 2 kg at R_C = 50 mm, Θ_C = 30^o

Radius B is 75 mm

Radius C is 50 mm

Mass of B is 5 kg

Mass of C is 2 kg

Find two masses, m_A and m_D that should be placed in planes A nad D respectively at radius 60 mm each, in order to balance the system.

Question 11: Label the cam-follower given, showing

(a) Base circle (b) Prime circle (c) Cam profile, (d) Pitch curve (e) pressure angle, and (f) follower.

Question 12: Find angular velocity ω (cw or ccw?) for bar AB?

1. If the unbalancing masses on a rotating shaft are all in the same plane, this is a called
a. Dynamic unbalance
b. static unbalance
c. Both a and b above
d. None of the above

2. Among the cam-and-follower system shown, which ones have an oscillating follower
a. A and B
b. A and C
c. B and C
d. C and d.

3. Among the cam and follower system shown which one has on offset follower

a. A
b. B
c. C
d. D

4. A flywheel is used on a rotating shaft to:
a. Reduce the changes in speed
b. Reduce the changes in torque
c. improve the efficiency

5. in a three force member the forces must all:
a. Be equal in magnitude
b. have the same direction
c. have direction passing through the same , concurrent point
d. none of the above.

Question 13:

The figure shows a plot of torque T vs crank angle Θ of an Engine over two revolution.

a) Calculate the total Energy input, U of the Engine over this angle range (note: change degrees into radians)
b) calculate mean torque T_m
c) The mean speed of the Engine is 100 rad/sec. If wish to have a coefficient of speed C_v = 0.05 what mass moment of inertia is suitable for the wheel?
d) Find the maximum speed and the minimum speed with this flywheel installed.

Question 14:

The unbalanced mass is in the next slide

m₁ = 12 kg m₂ = 3kg and m₃ = 10 kg

r₁ = 0.2 m r₂ = 0.3 r₃ = 0.15 m

ω = 750 rpm = 750*2 pi/ 60 = 78.5 rad/sec

Θ₁ = 0, Θ₂ = 135 Θ = 150

a) Find bearing reactions

b) Determine angle and calues of correcting mass mc if r_c = 0.25 m

Question 15: In the compound planetary gear train shown in the figure z₂ = 50 z₃ = 25 z₄ = 45 z₅ = 30 and z_e has 40 teeth. The arm rotaes clockwise w_arm = 50 rms and ω₆ = 20 rpm ccw.

a) find ω₃
b) find ω₂

Can you solve this all questions

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