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Kinematic Analysis & Synthesis (October 2010)

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Total No. of Questions : 12] [Total No. of Pages : 4 P1360 [3864] - 138 B.E. (Mechanical) KINEMATIC ANALYSIS AND SYNTHESIS (2003 Course) Time : 3 Hours] [Max. Marks : 100 Instructions to the candidates: 1) Answer three questions from Section - I and three questions from Section - II. 2) Answers to the two sections should be written in separate answer books. 3) Neat diagrams must be drawn wherever necessary. 4) Use of logarithmic tables slide rule, Mollier charts, electronic pocket calculator and steam tables is allowed. 5) Assume suitable data, if necessary. SECTION - I Q1) a) b) Derive formulas for the degree of freedom of planar and spatial mechanisms. State the limitations of these formulas. Give one example of an exception to the above formula. [8] Explain the following concepts with examples : i) Equivalent linkage. ii) [8] Kinematic Inversions in Planar Mechanisms. OR Q2) a) Explain Grashoff s Criterion of relative motion in a planar four bar mechanism. [6] b) Explain the terms Mechanical Advantage and Transmission Angle with reference to a four bar mechanism. Obtain an expression for the mechanical advantage, stating the assumption made, if any. [10] P.T.O. Q3) Crank O2 A rotates at 1 rad/s in clockwise direction. Given O2 A = 2 cm, AB = 8.5 cm, BC = 7.5 cm, CD = 5.25 cm, O5C = 7 cm, O2O5 = 7 cm. The line of action of slider D is at a perpendicular distance of 5 cm from point O5. Use the auxiliary point method to obtain the velocity and acceleration of any one point on link BCD. Refer fig (1). [16] OR Q4) a) b) Q5) a) b) Explain the complex algebra method for displacement, velocity and acceleration analysis of a Crank and slotted lever quick return mechanism. Explain how the resulting equations are solved. [10] State and explain Freudenstein s theorem. [6] State any two forms of Euler-Savary Equation and discuss their significance and uses with reference to the rolling motion of the moving centrode over the fixed centrode. [10] Explain how Curvature theory is used in Synthesizing dwell linkages to replace Cam-follower mechanisms. [8] OR Q6) a) Explain with neat sketch the Bobillier construction for drawing inflection circle for motion of connecting rod with respect to frame in a slider Crank mechanism. Show all construction lines. [10] [3864]-138 2 b) Write note on any two : i) Ball s point any its uses. ii) Fixed and Moving centrodes. iii) Hartmann Construction. [8] SECTION - II Q7) Synthesize a 4 bar function generator to generate the function y = 1/x in the interval 1 x 2 using pole method. Taking starting position of input link as 45 , range of motion for input link = 60 and range of motion for output link = 90 . Use three accuracy points with chebychev spacing. [16] OR Q8) Synthesize slider Crank mechanism in which the slider displacement is proportional to the square of Crank rotation. Si Ss i s = Sf Ss f s 2 where, starting positions of Crank and slider are s = 45 and Ss = 8 cm respectively. Also range for Crank rotation and linear displacement of slider are = 60 and S = 4 cm respectively. Use three accuracy points with chebychev spacing. Use Graphical method. [16] Q9) a) Determine the link lengths of a 4 bar linkage using Freudenstein s equation, that satisfies following specifications in one of its positions : 2 = 60 2= 5 rad/sec 4= 2 rad/sec 2= 2 rad/sec2 b) 4= 90 4= 7 rad/sec2 Subscripts 2 and 4 represents input and output link respectively. The length of the input link is to be unity. [10] State and prove Roberts-chebychev theorem. [6] [3864]-138 3 OR Q10)a) Using complex number method, synthesize a four bar linkage that satisfies following specifications in one of its position : 2 = 15 rad/sec 2 = 0 rad/sec2 3 = 6 rad/sec 3 = 85 rad/sec2 4 = 8 rad/sec 4 = 160 rad/sec2 Draw the mechanism obtained obove. b) Q11)a) b) Explain Double point and Symmetry of a Coupler Curve. [10] [6] Explain Transformation matrix method of displacement analysis of spatial mechanisms. Obtain displacement relationship for Hooke s joint. [10] Write a note on - Eulerian Angles. [8] OR Q12)a) b) Classify various types of Spatial mechanisms and mention their applications. [8] Obtain an expression for the transformation matrix relating two cartesian frames which are translated and rotated with respect to each other.[10] vvvv [3864]-138 4

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