Midterm 1_Sample

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San Jose State University *

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154

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Mechanical Engineering

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Apr 3, 2024

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San Jose State University ME 154 – Spring 2019 Name: MIDTERM EXAM 1  Time allocation: 100 minutes  Maximum points: 50  All work is to be completed strictly on an individual basis  The use of a compass, protractor and a ruler is permitted. No sharing is allowed.  Required formulae are given with each problem. No other cheat sheets are permitted.  This is a “ CLOSED BOOK ” exam and all the personal notes are prohibited. A scientific calculator is permitted, but any device with enhanced capability (e.g., communications, image storage) is subject to denial at the proctor’s discretion. The use of any other electronic devices (smart phones, smart watches, digital pens, tablets etc.) during the exam is prohibited and subject to confiscation. Any viewing or use of aids (notes, electronic device, or otherwise) is reportable as suspicion of cheating to the Office of Student Conduct and Ethical Development.  In the event of a building emergency that requires site evacuation before the exam time ends, place this exam at your desk and evacuate according to standard emergency procedures. If safety constraints allow, the exam may be collected and graded “as-is”, but the weighing of the exam relative to the other coursework will be adjusted based on the circumstances. Academic Integrity Reminders:  I will not take an exam in place of someone else, or have someone take an exam in my place.  I will not give information or receive information from an unauthorized source during an exam.  I will not use more reference material during an exam than is allowed by the instructor.  I will not obtain a copy of the exam prior to the time it is given.  I will not alter an exam after it has been graded and return it to the instructor for regrading. 1

Q1. For the following questions, provide your brief answers: (1 point each) (a) Define the term “kinematic inversion” in the context of ME 154. (b) How many DOFs does a helical joint have? (c) True or false? By changing the ground link, we can change a non-Grashof mechanism to a Grashof mechanism (d) What is the importance of transmission angle? (e) Intermittent motion is a sequence of motions and dwells. Define the term “dwell.” (f) What are the advantages of using a fourbar mechanism instead of a cam? (g) What is a cusp on a coupler curve? Draw a coupler curve with a cusp. (h) Why a fourbar mechanism cannot have a time ratio of 1:3? (i) Define the term “Mobility” of a mechanism in the physical context of ME154. (j) True or false? Complete shrinkage of a ternary link will change the DOF. 2

Q2. Mobility (4 points each) For the mechanisms shown on this page, determine their DOFs (mobility). Show your accounting for L , J 1 , J 2 . Given: M = 3 (L- 1 ) – 2 J 1 – J 2 3

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Q3. Coupler Curve and Position Analysis (6 points) We need a point on a fourbar mechanism to follow the path circled in the following partial atlas. a. Find the lengths of all the links and the position of coupler point. (3 points) b. Plot a schematic of the mechanism at an arbitrary position. (3 points) 4

Q4. Graphical Synthesis (10 points) Design a four-bar linkage to move line PQ on its ROCKER through the two extreme positions as shown. The dyad limiting the movement of the mechanism between the two positions, must guarantee that the forward motion takes 1.4 times longer than the return motion. Identify the fixed pivot points (O 2 and O 4 ) and specify the length of each member in your design. Examine the Grashof condition (no need to reiterate if you find that it is not a Grashof mechanism). 5

Q5. Analytical Synthesis (8 points) (a) True or false: Assuming the diagram represents a three- position analytical synthesis problem, the length of vector W 1 is always the same as the length of vector W 3 . (1 point) (b) Write the right -side dyad vector loop equation that includes the vector P 31 . While any legitimate vector loop could potentially be helpful, this question asks specifically for the one that directly assists in analytical linkage synthesis between positions 1 and 3. (2 points) (c) Now rewrite the same equation using complex numbers . Use the lowercase expressions for lengths (“ u ” is the length of U , “ p 31 ” is the length of P 31 , and so on) . (3 points) (d) The two distinct vector loops relating positions 1 and 2 and relating positions 1 and 3 (both considering only the right side of the mechanism) would produce 12 variables: u ,  ,  2 ,  3 , s,  ,  2 ,  3 , p 21 , p 31 ,  2 , and  3 . Assuming that 6 of the variables are specified in the problem statement: (a) identify how many independent scalar equations are available from these two vector loops to solve for unknowns, (b) identify how many “free-choice” variables remain. (2 points) 6

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Q6. Mechanism Analysis (8 points) Determine the position, velocity, and acceleration of point P on the mechanism shown below at an instantaneous position when θ 2 = 60°. Link 2 rotates at a constant ω 2 = 40 rad/s. 7

EQUATIONS POSITION ANALYSIS VELOCITY ANALYSIS PA A P R R R      ) ( 3 3     j PA pe R  PA A P V V V        ) ( 3 3 3      j PA pe j V  Positive sign for crossed circuit and negative for open 8