JNTU
JNTU B.Tech II KINEMATICS OF MACHINERY Previous Question Paper (November/December - 2020 - R13)
Answer any Five Questions. All Questions Carry Equal Marks.
Main
Show that the linkages shown in Figure 1 are structures.
Answer
A linkage is classified as a structure if it has zero degrees of freedom, meaning it cannot undergo any relative motion between its links. According to the Kutzbach criterion, the degree of freedom (F) of a mechanism is given by:
Where n is the number of links, j is the number of binary joints, and h is the number of higher pairs. For a structure, F must be less than or equal to zero. In the provided linkages, the number of links and joints results in a value of F ≤ 0. Specifically, if the number of links is n and the number of joints is j, and the configuration is such that the constraint equations equal the number of degrees of freedom, the links are locked in position, forming a rigid frame or structure rather than a mechanism.
Which inversion of the double-slider crank chain is used to convert rotary motion to reciprocating motion? Draw a neat sketch of it, and explain how it works.
Answer
The inversion of the double-slider crank chain used to convert rotary motion to reciprocating motion is the Elliptical Trammel. In this mechanism, the two sliders move in two perpendicular slots, while the connecting link rotates.
Working Principle: As the link rotates, the two sliders move back and forth in their respective perpendicular guides. If a point is marked on the connecting link (or an extension of it), it traces an ellipse. This mechanism is primarily used to generate elliptical paths or to convert the rotary motion of the crank into the reciprocating motion of the sliders.
Sketch Description: Imagine a horizontal slot and a vertical slot intersecting at a center point. A link with two sliders at its ends is placed such that one slider is constrained in the horizontal slot and the other in the vertical slot. As the link rotates, the sliders perform reciprocating motion within their guides.
Sketch and explain the Oldham coupling as an inversion of the double-slider crank chain.
Answer
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Draw and explain the Klein’s construction to obtain the velocity and acceleration of the slider in a reciprocating engine mechanism. Assume suitable dimensions for the link lengths of the mechanism. Give the necessary proof.
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In the mechanism shown in Figure 2, the crank AB is 15 cm long. BC = CD = 45 cm; DE = 15 cm; AG = DG = EF = 37.5 cm; HF = 10 cm; the crank is rotating clockwise at 240 rpm. Find the velocity of the slider at F by the Instantaneous Centre method.
Answer
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In the Robert mechanism shown in Figure 3, AB = BC = CD = (AD/2). Locate the point P on the central vertical arm that approximately describes a straight line path.
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Prove that the Davis steering gear satisfies exactly the condition for correct steering.
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Draw the profile of a cam to raise a valve with SHM through 40 mm in 1/4th of the cam rotation, keep it fully raised through 1/10th of the cam rotation, and to lower it with uniform and equal acceleration and retardation in 1/6th 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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An epicyclic gear train, as shown in Figure 4, is composed of a fixed annular wheel A having 150 teeth. The wheel A is meshing with wheel B which drives the wheel D through an idle wheel C, D being concentric with A. The wheels B and C are carried on an arm which revolves clockwise at 100 rpm about the axes of A and D. If the wheels B and D have 25 and 40 teeth respectively, find the number of teeth on C and the speed and sense of rotation of C.
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