# CITY UNIVERSITY SCHOOL OF ENGINEERING AND MATHEMATICAL SCIENCES

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1 CITY UNIVERSITY SCHOOL OF ENGINEERING AND MATHEMATICAL SCIENCES AERONAUTICAL ENGINEERING MEng/BEng (Hons) AIR TRANSPORT ENGINEERING MEng/BEng (Hons) AIR TRANSPORT ENGINEERING BSc (Hons) AUTOMOTIVE AND MOTOR SPORT ENGINEERING MEng/BEng (Hons) AUTOMOTIVE AND MOTOR SPORT TECHNOLOGY BSc (Hons) MECHANICAL ENGINEERING MEng/BEng (Hons) ENGINEERING AND ENERGY MANAGEMENT MEng/BEng (Hons) PART II Examination Mechatronics [ME2106] Date: May 2007 Time: 3 hours Answer SIX Questions - TWO from each section Page 1 of 10

2 Question 1 SECTION A DYNAMICS A trolley has a mass m and rests on frictionless wheels, Fig Q1. The trolley is connected to a base by a damping element with damping constant c and a system of two identical springs of constant k (see the figure). The trolley was observed to oscillate harmonically in free vibration with the natural frequencyω. n Fig Q1 Considering that the base undergoes harmonic motion: y ( t ) Y ( ωt ) mass m has a response x(t): = sin 0 and that the Hint: (i) Compute the equivalent stiffness of the springs. [3 Marks] (ii) Draw the free body diagram for the mass m. (iii)state the equation of motion. (iv) What is the significance of Y 0 in the expression y ( t ) = Y sin 0 ( ωt )? What is the generic expression for the motion of the cart motion x(t)? (v) Draw the Phasor Diagram for the given system. k = k 1 + k 2 Page 2 of 10

3 Question 2 A disc with the inertia I 0 is liked to base using a shaft with stiffness k and damping constant c, Fig Q2. The base of this single-degree-of-freedom system undergoes θ t = Θ sin ωt. Considering that the disk I 0 has a response harmonic motion: y ( ) y ( ) θ ( t) x L θy I o θx k, c Fig Q2 Base (i) Draw the free body diagram for the disc I 0 (ii) State the equation of motion. [4 Mark] = Θ sin ωt? (iii)what is the significance of ω in the expression θ ( t) ( ) (iv) Draw the Phasor Diagram for the given system. [13 Marks] y y Page 3 of 10

4 Question 3 In the single-degree-of-freedom system Fig Q3 the mass m and the spring constants k are known. The coefficient of viscous damping c is not known. However, it is known that the system is under-damped. Hints: T = Fig Q3 (i) Compute the equivalent stiffness of the springs.. (ii) Compute the natural frequency for the system. (iii)define the viscous damping factor Which condition should it fulfill? (iv) It is known that the motion of mass m can be described by. ζω ( ) n = t cos ( ω φ ) x t Ce t An experimental record showed that for two successive oscillations, the xi amplitude drop can be expressed as: = A. Considering that for the two x + oscillations the maximum amplitude is reached at t i and t = i 1 t + + i T, respectively, determine an expression for the viscous damping factor as a function of ω and T. n (v) What is the significance of ω d in equation (1)? Express it as a function of ω n and ζ. [3 Marks] 2π ωd i 1 d k = 1 1 / k + k / 2 k = k 1 + k Page 4 of 10

5 Question 4 Consider the undamped, 2 degree of freedom system represented in Fig Q4. Using the notations in the figure (where: k 1 = k 2 = k 3 = k and m 1 = m 2 = m): (i) Draw the free body diagram for each body (ii) State the equations of motion (iii) State the characteristic equation [9 Marks] (iv) Compute the eigenvalues (v) Compute the natural frequencies x (t) 1 k 1 m 1 k 2 m2 x (t) 2 k 3 FigQ4 Page 5 of 10

6 Question 5 Considering the mechanism shown in fig Q5 (where the length of each element is written next to it) Fig Q5 (i) Compute the number of degrees of present in the system: (ii) Determine if at least one link is capable of making a full revolution (iii) Calculate the output position and the angular velocity ratio for input values of 90 o [15 Marks] Hints: It is known that : arctan A A B C ψ = + B + C ψ& sin ( φ ψ ) K1 sinφ = & φ sin φ ψ K sinφ where : ( ) 2 d K1 = c A = sinφ d K2 = B = cosφ K2 a C = K cosφ K a b + c + d K3 = 2ac Page 6 of 10

7 SECTION B MICROPROCESSORS Question 6 a) A microprocessor has a reboot address of 0000 Hex. Draw a suitable memory map for a system with 4k ROM and 1kRAM [ 5 Marks] b) Design an address decoding circuit for question 6a c) Explain how the FETCH-EXECUTE cycle transfers data from memory to the CPU ( or microprocessor unit ) Question 7 a) Why is it necessary to use a handshaking protocol when interfacing a mechanical device, such as a printer to a computer system? [2 Marks] b) Explain clearly, with a circuit diagram and a software flowchart, how the handshaking for a parallel printer port works c) What, essentially is the difference between polling and interrupts? [3 Marks] d) What happens to the SP ( Stack Pointer ) and PC ( Program counter ) during a hardware generated interrupt cycle? Question 8 (a) How can a simple length of thin wire be used to measure mechanical strain? (b) How can a strain gauge be interfaced to a computer? (c) Four identical strain gauges are mounted on a cantilever beam and interfaced to a computer. (i) Explain how calibrate the experiment [5Marks] (ii) How could the same experiment be used to measure mechanical vibrations? [ 5 Marks] Page 7 of 10

8 Question 9 What is a USB and how does it work? You answer should include the concepts of plug and play, collision detection, data transfer protocols, device drivers, operating system, and unique addresses [25 Marks] Question 10 (a) What are:- (a) ROM (b) RAM (c ) EPROM (d) PROM, (e) FLASH (b) Draw the circuit diagram, truth table and Boolean equation for the following 2 input logic gates:- a. AND b. OR c. NOR d. NAND (e) XOR [15 Marks] (c) Write down the truth table, circuit diagram and Boolean equation for an NOT gate. How many inputs are there? [ 4Marks] (d) What is an XOR gate used for? [1Mark] Page 8 of 10

9 SECTION C CONTROL Question 11 (a) Define two parameters which we can use to measure the performance of an analogue control system. [ 2 Marks] (b) What are Poles and Zeros? [ 3 Marks] (c) A DC servo motor has an armature resistance of R a Ohms, a motor torque constant k m and a back emf constant k b. The motor is connected to a mechanical load with inertia J and viscous damping factor D. Find the transfer function in the s domain. ( take system input as the voltage applied to the motor ( volts) and the position of the motor shaft (radians) as output. (d) Draw the block diagram of a position control system with feedback H(s)=1, and same motor and load as Q11(c ) (e) Find the transfer function of s suitable lag/lead compensator. Question 12 (a) Write down the standard form of the general second order transfer function (b) Discuss the response of the general second order T.F. to a STEP input signal [6 Marks] (c) A general first order Transfer Function is given by G(s) = k/(s+a) Calculate the step response, in the time domain. Note:- step response in the s domain is 1/s and the Laplace transform of 1/(s+a) is e -at [15 Marks] Page 9 of 10

10 Question 13 An automobile suspension system can be modelled as a mass m hung vertically from a spring stiffness k and a shock absorber c. (a) Draw the free body diagram and obtain the equation of motion [ 5 Marks] (b) Take the upward force F as the input and displacement of the mass, x, as output, calculate the transfer function (c) Prove the system is UNCONDITIONALLY STABLE [15 Marks] Question 14 Why is Failure Modes And Effects Analysis important in the design of aircraft and automobile control systems? Your answer should explain the concept of a SOFTWARE GEARBOX and compare the advantages and disadvantages of mechanical control systems as compared with microprocessor based systems. [25 Marks] Internal Examiners : Dr R.C. Edney Dr M. Teodorescu External Examiners: Professor R. Crookes Page 10 of 10

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