JAWAHARLAL NEHRU TECHNOLOGICAL UNIVERSITY HYDERABAD
JAWAHARLAL NEHRU TECHNOLOGICAL UNIVERSITY HYDERABAD B.Tech II Year KINEMATICS OF MACHINES Previous Question Paper (March - 2022 - R13)
Answer any five questions. All questions carry equal marks.
Main
What is a kinematic inversion? Explain, with a sketch, an inversion of four bar chain.
Answer
A kinematic inversion is the process of fixing different links of a kinematic chain one by one to obtain different mechanisms. A kinematic chain with n links can produce n distinct mechanisms by fixing each link in turn.
The four-bar chain consists of four links connected by four turning pairs. By fixing the shortest link (crank), we obtain the crank-rocker mechanism. If the link adjacent to the shortest link is fixed, we obtain a drag-link or double-crank mechanism. If the link opposite to the shortest link is fixed, we obtain a double-rocker mechanism.
Sketch description: A four-bar chain consists of links AB, BC, CD, and DA connected at joints A, B, C, and D. In the crank-rocker inversion, link AD (the frame) is fixed, link AB acts as the crank rotating fully, and link CD acts as the rocker oscillating about point D.
A double slider mechanism is used to draw an ellipse with major axis equal to 20 cm and minor axis 15 cm. Set out the mechanism, and draw the locus of the points tracing the required ellipse.
Answer
A double slider-crank mechanism, specifically the elliptical trammel, is used to draw ellipses. The mechanism consists of a frame with two perpendicular slots and a bar with two sliders moving in these slots.
Given: Major axis (2a) = 20 cm, so semi-major axis a = 10 cm. Minor axis (2b) = 15 cm, so semi-minor axis b = 7.5 cm.
To set out the mechanism:
- Draw two perpendicular lines representing the X and Y axes (the slots).
- Take a rod of length equal to the semi-major axis (10 cm).
- Mark a point P on the rod such that the distance from the end of the rod to P is the semi-minor axis (7.5 cm). The distance from P to the other end of the rod is then 10 - 7.5 = 2.5 cm.
- Place the sliders at the ends of the rod into the perpendicular slots.
- As the rod moves, point P traces an ellipse with semi-major axis 10 cm and semi-minor axis 7.5 cm.
The locus of point P is defined by the coordinates x = a cos(θ) and y = b sin(θ), which satisfies the equation of the ellipse: (x²/a²) + (y²/b²) = 1.
Distinguish between constrained motion and unconstrained motion, with suitable examples.
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In a crank and slotted lever mechanism, the driving crank is 35 mm long, and the time ratio of cutting stroke to return stroke is 1.6. If the length of working stroke of the ram is 110 mm, find the distance between the fixed centers, and the slotted lever length.
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A toggle press mechanism, shown in Figure 1, has dimensions of various links (in mm) as follows: OP = 50; RQ = RS = 200; PR = 300; Find the linear velocity of S, and the angular velocities of the links RQ and RS, when the crank OP rotates at 60 rpm ccw. Solve by the relative velocity method.
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What is ‘Coriolis component of Acceleration’? When is it present? Explain.
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In a four bar mechanism shown in Figure 2, the crank AB rotates with an angular velocity of 100 rad/s and an angular acceleration of 4400 rad/s2 (both ccw) at the instant when the crank makes an angle of 75° with the horizontal. AD = 110 mm, AB = 75 mm, BC = 85 mm, CD = 100 mm, BE = 35 mm, CE = 60 mm, CQ = 65 mm. (Q is a point on BC). Draw the acceleration polygon, and find the accelerations of the points E and Q, and the angular acceleration of the link BCE.
Answer
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For a Hooke’s joint, prove that the speeds of the two shafts will be equal if tanθ=±√cosα, where α = angle of inclination of the driven shaft with the driving shaft, and θ is the angle turned by the driving shaft at any instant.
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Discuss the advantages and disadvantage of Davis steering gear vis-à-vis Ackermann steering gear.
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What is a Pantograph? Draw a neat sketch of the mechanism and give the necessary proof to show how it copies a profile.
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Two shafts are coupled together by a Hooke’s joint, the driving shaft rotating uniformly at 500 rpm. Find the greatest permissible angle between the shafts if the maximum speed of the driven shaft is 530 rpm. Prove your reasoning. What is the minimum speed of the driven shaft?
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What are the cams with specified contours? Why are they necessary? Explain their advantages and disadvantages.
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Draw the profile of a cam to raise a valve with SHM through 40 mm in (1/4)th of the cam rotation, keep it fully raised through (1/10)th of the cam rotation, and to lower it with uniform and equal acceleration and retardation in (1/6)th of the cam rotation. The valve remains closed during the rest of the cam rotation. The diameter of roller follower is 20 mm, and the minimum radius of cam is to be 30 mm. The axis of the follower passes through the axis of the cam shaft.
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A pinion having 18 involute teeth of 4 mm module pitch rotates at 240 rpm and transmits 2.5 HP to a gear wheel having 54 teeth. The addendum on both the wheels is 0.3 times the circular pitch, and the pressure angle is 18°. Find the length of the path of approach and arc of approach.
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A simple Epicyclic gear train is shown in the figure 3. Deduce, from fundamentals, the expression for velocity ratio of the gear train.
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