Linkages and Mechanisms(2)

Elliptical trammels

It is an instrument used for drawing ellipses. This inversion is obtained by fixing the slotted plate i.e. link 4 as shown in fig. The fixed plate or link 4 has two straight grooves cut in it, at right angles to each other. The link 1 and link 3, are known as sliders and form sliding pairs with link 4. The link AB link 2 is a bar which forms turning pair with links 1 and 3.

Fig: Elliptical trammels

When the links 1 and 3 sslidesalong their respective grooves, any point on the link 2 such as P traces out ellipse on surface of link 4 that shown in fig(a) . A little consideration will show that AP and BP are the semimajor axis and semiminor axis of the ellipse .

Scotch yoke mechanism

This mechanism is used for converting rotary motion to reciprocating motion. This inversion is obtained by fixing either the link of 1 or link of 3. In fig the link 1 is fix. In that mechanism when the link of 2 which corresponds to crank rotates about B as centre, the link 4 which is same to aframe reciprocates. That fixed link 1 guides the frame.

Fig:Scotch yoke mechanism

Oldham’s coupling

An oldham's coupling is used for connecting two parallel shafts whose axes are at a small distance apart. The shafts are coupled in that if one shaft rotates then the other shaft also rotates at the same speed. This inversion is made by fixing the link 2 as shown in Ffg (a) . The shafts to be connected have two flanges link 1 and link 3 rigidly withfastened at their ends by forging.

The link 1 and link 3 form turning pairs with link 2. These flanges have diametrical slots cut in inner faces which is shown in fig (b) . The intermediate piece (link 4) which is a circular disc with two tongues i.e. diametrical projections T1 and T2 on each face at right angles to each other, as shown in Fig (c) . The tongues on the link 4 neartly fit into the slots in two flanges link 1 and link 3. The link 4 can slide or reciprocate in the slots in the flanges.

Fig Oldham’s coupling.

When the driving shaft A is rotated, the flange C causes the intermediate piece link 4 to rotate at the same angle through the flange has rotated and it further rotates the flange D link 3 at the same angle and thus the shaft B rotates. Hence the links 1, 3 and 4 have the same angular velocity at every time. A little consideration will show, that there is a sliding motion between link 4 and each of another links 1 and 3.

Whitworth quick return motion mechanism

This mechanism is usually used in shaping ,slotting machines. In thismechanism the link CD (link 2) forming the turning pair is fixed as shown in fig. The link 2 same to a crank in a reciprocating steam engine. The driving crank CA i.e. link 3 rotates at uniform angular speed. Then the slider (link 4) attached to the crank pin at A slides along the slotted bar of PA (link 1) which oscillation at a pivoted point D. The connecting rod PR carries the ram at R to which a cutting tool is fixed onpoint. The motion of tool is constrained along the line RD produced, i.e. along a line passing through D and perpendicular to CD.

Fig:Whitworth quick return motion mechanism

Straight Line Motion Mechanisms

A mechanism built in such a manner that a particular point in it is constrained to trace a straight line path within the possible limits of motion, is known as a straight line motion mechanism.

Scott Russel Mechanism

This mechanism is shown in Figure. It consists of a crank OC, connecting rod CP, and a slider block P which is constrained to move in a horizontal straight line passing through O. The connecting rod PC is extended to Q such that ,

PC= CQ= CO

Fig:Scott Russel Mechanism

It will be proved that for all horizontal movements of the slider P, the locus of point Q will be a straight line perpendicular to the line OP. Now draw a circle of diameter PQ as shown. It is will know that diameter of a circle always subtends a right angle or any point on the circle. Thus, at point O, the angle QOP is a right angle. For any position of P, the line connecting O with P will always be horizontal. Therefore, line joining the corresponding position of Q with O will always a straight line perpendicular to OP. Thus, the locus of point Q will be straight line perpendicular to OP. Thus, a horizontal straight line motion of slider block P will enable point Q to generate a vertical straight line, both passing through O.

Hook’s Joint or Universal Coupling

Fig:Universal Coupling

Chamber wheels

In this mechanism mainly the two types lobes. Two lobes operates inside the casing.

Fig: Chamber wheels

Synthesis concepts

Applying synthesis concept will create an extensive range of mechanisms. Then analysis techniques will allows to simulate and see the motion of mechanisms, (velocities, accelerations, forces, etc. and also to verify that they are useful. The level of concepts is adequate for all different specialties of engineering. The Synthesis concepts commonly applied to the analysis and synthesis of mechanisms and is oriented to its application by means of computer science programs. The objective of synthesis concept is practice implementation of the knowledge and techniques acquired, by means of practical exercises of application in the industry and mechanical engineering and technical analysis of mechanisms.

References:
1. H.H. Mabie and C. F. Reinholtz, “Mechanism and Dynamics of Machinery”, Wiley.
2. J.S. Rao & R.V. Dukkipati Mechanisms and Machine Theory, New Age International (P) Limited..
3. J.E. Shigley and J.J. Uicker, Jr., “ Theory of Machines and Mechanisms”, McGraw Hill.
4. B. Paul, “Kinematics and Dynamics of Planar Machinery”, Prentice Hall.
5. C. E. Wilson, J.P. Sadler and W.J. Michels, “Kinematics and Dynamics of Machinery”, Harper Row.