Dynamics and Kinematics

PhD Qualifying Exams

DYNAMICS AND KINEMATICS

Summer-2007 Winter-2007 Spring-2006 Winter-2006 Spring-2005 Winter-2005 Spring-2004 Winter-2004 Winter-2003 Winter-2002 Spring-2001 Spring-2001 Winter-1999 Spring-1999 Winter-1998 Spring-1998 Winter-1998 Spring-1998 Spring-1996 Winter-1996

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Department of Mechanical Engineering Ph. D. Qualifying Examination

Kinematics and Dynamics

Fall, 2007

1) There are 6 problems, but the problems are not equally weighted. They are also not equally

difficult. Be sure to work each one. 2) Start each problem on a separate page. 3) Work as much as possible on the problem sheets. 4) Be sure to write your ID number and the problem number on the front of each page that you

use. 5) In some cases, insufficient information may be given to enable the student to demonstrate

his/her ability to make engineering assumptions.

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Problem 1 (15 points):

End A of the uniform 5-kg bar is pinned freely to the collar, which has an acceleration a = 4 m/s2 along the fixed axis shaft. If the bar has a clockwise angular velocity ω = 2 r/s as it swings past the vertical, determine (a) the angular acceleration of the bar at this instant and (b) the components of the force acting at A at this instant. The moment of inertia of a slender bar about its

mass center is 2121 mLI = .

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Problem 2 (15 points): A 2-kg sphere A translating at 4 m/s strikes the end of a 5-kg slender bar B. The bar is pinned at O. What is the angular velocity of the bar immediately after impact if the coefficient of restitution is e = 0.8?

ID Number________________________ Problem 3 (15 points): The slender beam AB having a mass of 100 kg is initially in the vertical position (θ = 0°) when a constant force of P = 2 kN is applied. Determine the angular velocity of the beam when it has rotated by θ = 30°.

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Problem 4 (30%)

a) Design a single-stage planetary gear train to maximize the speed reduction if the ring gear is fixed and has a pitch diameter of 4 inches with a diametral pitch of 20. Sketch your design and provide the pitch diameters for all of the clearly identified gears.

b) Using only gears identical to those from the planetary gear train, design a simple gear train that approximates the speed reduction of the planetary gear train as closely as possible with the fewest number of gears. Sketch your design and provide the pitch diameters for all of the clearly identified gears.

c) Using only gears identical to those from the planetary gear train, design a compound gear train that meets or exceeds the reduction of the planetary gear train with the fewest number of gears. Sketch your design and provide the pitch diameters for all of the clearly identified gears.

d) If the efficiency of every gear mesh is 98%, what is the overall efficiency of each of your three designs?

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Problem 5 (15%) In the mechanism shown, the angular velocity of link 2 is 5 rad/sec CCW (constant).

1) Determine the velocity and acceleration of link 6 2) Now change the location of the fixed pivot at C along the line defined by BD so that the

velocity of link 6 is equal and opposite to the velocity computed in step 1.

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Problem 6 (10%) Assume that the six bar mechanism is drawn to scale. Link 2 rotates with an angular velocity of 100 rpm in the counterclockwise direction.

i) Determine the magnitude and direction of the angular velocity of link 5. ii) If link 2 is driven by a torque (counterclockwise) of 10 in-lbs, what is the torque on link 5

required for equilibrium