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# Note for Kinematics of Machinery - KM by Rohit Sriram

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#### Note for Kinematics of Machinery - KM by Rohit Sriram

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ME6401-Kinematics of Machinery Mechanical Engineering 2014-2015 UNIT 1 – BASICS OF MECHANISM PART A 1. Differentiate between Machine and Mechanism. Machine Mechanism Machine is a mechanism or collection of Combination of rigid or resistant bodies mechanism which transmits force from the connected that they move upon each other source of power to the resistance (load) to with definite relative motion, overcome and thus performs useful mechanical work. Eg. Lather, Shaping Machine etc. Eg. Single slider mechanism in IC engine All machines are mechanism All mechanism are not machine 2. Write down Kutzbach criterion to find the mobility of a planar mechanism. The Kutzbach criteria which calculates the mobility. F = 3(n – 1) – 2j – h ; Where, F- Degrees of freedom, n – number of links, J – number of joints, h – no of higher pairs 3. Define transmission angle and its significance. The acute angle between the coupler and the driven link. In Figure, if AB is the input link, the force applied to the output link, CD, is transmitted through the coupler link BC. (That is, pushing on the link CD imposes a force on the link AB, which is transmitted through the link BC.) For sufficiently slow motions (negligible inertia forces), the force in the coupler link is pure tension or compression (negligible bending action) and is directed along BC. For a given force in the coupler link, the torque transmitted to the output bar (about point D) is maximum when the angle between coupler bar BC and output bar CD is /2. Therefore, angle BCD is called transmission angle. When the transmission angle deviates significantly from /2, the torque on the output bar decreases and may not be sufficient to overcome the friction in the system. For this reason, the deviation angle =| /2- | should not be too great. In practice, there is no definite upper limit for , because the existence of the inertia forces may eliminate the undesirable force relationships that is present under static conditions. Nevertheless, the following criterion can be followed. 4. Enumerate the difference between a Machine and a Structure. [Anna University, June 2014] Machine Machine is a mechanism or collection of mechanism which transmits force from the source of power to the resistance (load) to overcome and thus performs useful mechanical work. Structure Structure is the assemblage of resistant bodies without any relative motion between the links. Eg. I C Engine Eg. Bridges & Dams 5. List out the inversions of a double slider crank chain. Inversions of Double Slider Mechanism - First Inversion – Scotch Yoke mechanism, Second Inversion – Oldhams Coupling , Third Inversion – Elliptical trammel, Fourth Inversion – Hand Pump 6. State Grashof’s law for a four bar linkage.[Anna University, December 2012] It states that for a planar four bar linkage, sum of the shortest and longest link – lengths must be less than or equal to the sum of the remaining two link-lengths, is there is to be a continuous relative motion between two members - S + L ≤ P + Q ; Where, S – Length of shortest link, L – length of longest link, P and Q – remaining two link lengths. i) If L + S < P + Q, then we call this a Grashof Mechanism G.1 = crank-rocker if S is the crank and either of the adjacent link is the fixed link G.2 = double-crank if S is the fixed link G.3 = double-rocker if the link opposite S is the fixed link ii) If L + S > P + Q, then we call it non-Grashof’s mechanism only double-rocker: no link is St.Joseph’s College of Engineering / St Joseph’s Institute of Technology 1 ISO 9001: 2008

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ME6401-Kinematics of Machinery Mechanical Engineering 2014-2015 capable of making a complete revolution iii) If L + S = P + Q, it can have G.1~G.3 and parallelogram form (collinear) 7. Define degree of freedom (or) mobility and give the DOF for a shaft in a circular hole. It is defined as the minimum number of input parameters which must be independently controlled, inorder to bring the mechanism into a useful engineering purpose. DOF for a shaft in circular hole is 2. It will have sliding motion and rotational motion. If the shaft end is fixed to a collar, sliding motion will be arrested and DOF is 1. 8. Define kinematic pair and illustrate any two types of constrained pair. When two kinematic links are connected in such a way that their motion is either completely or successfully constrained, these two links are said to form a kinematic pair. E.g foot step bearing, circular shaft in the circular slot 9. Define Pantograph. A pantograph is a mechanism used to produce paths on an enlarged or reduced scale as exactly as possible the path described by a given point. It is based on four bar kinematic chain 10. Define Link and List the various type of link. Link is a resistant body is one which is capable of transmitting the required motion and force with negligible deformation in the direction of force transmission. Types of links: 1) Rigid Link 2) Flexible link 3) Fluid link 11. Define the kinematic chain. Kinematic chain is defined as the combination of kinematic pairs in which each link forms a pair of two kinematic pairs and the relative motion between the links is either completely constrained or successfully constrained. When a number of links connected in space make relative motion of any point on a link with respect to any other point on the other link follow a definite law it is known as kinematic chain. 12. Name the inversions of four bar mechanisms. Inversions of four bar mechanisms - First Inversion – Coupled wheels of locomotive – double crank, Second Inversion – Beam Engine - Crank and lever mechanism, Third Inversion – Watt’s Engine Indicator – Double lever mechanism. 13. Name the inversions of single slider mechanism. Inversions of Single Slider Mechanism - First Inversion – Reciprocating engine mechanism, Second Inversion – Gnome Engine or Rotary Engine – Whitworth quick return mechanism, Third Inversion – Quick return mechanism – Crank and slotted lever – Oscillating cylinder engine, Fourth Inversion – Hand Pump. 14. Name some straight line generating mechanism. Straight line generating Mechanism – Peaucellier mechanism, Scott Russel mechanism and Hart’s mechanism, Robert’s Mechanism & Tchibicheff Mechanism. 15. Write down the Grubler’s criteria for planar mechanism. The following equation is used to describe mobility in 2D or planar systems: M = 3(N-1) – 2 f1 – f2, Where, N = total number of links, M = DOF, f1 = number of 1 DOF joints, f 2 = number of 2 DOF joints This is known as GRUBLER’S EQUATION and is for mobility of planar systems. 16. Define Kinematic Pair. When two links are in contact with each other it is known as a pair. If the pair makes constrain motion it is known as kinematic pair. 17. Classify the kinematic pair based on the various characteristics. Kinematic pairs are classified on the basis of the following characteristics – 1) Type of relative motion between contacting elements, 2) Type of contact between contacting elements, 3) Number of degrees of freedom and 3) Type of closure. 18. Define Higher and lower pair. Kinematic pairs in which there is a surface (area) contact between the contacting elements. All revolute pairs, sliding pairs, screw pairs, globular pairs, cylindrical pairs and flat pairs are Lower Pairs. Kinematic pairs in which there is a point or line contact between the contacting elements are called as higher pair. Meshing gear teeth, cam and follower pair, wheel rolling on a surface, a ball and roller bearings and pawl and ratchet are higher pair. 19. Define kinematic inversion. A mechanism is formed by fixing one of the links of a chain. The process of choosing different links St.Joseph’s College of Engineering / St Joseph’s Institute of Technology 2 ISO 9001: 2008

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ME6401-Kinematics of Machinery Mechanical Engineering 2014-2015 of a kinematic chain for making different kind of mechanism is called Kinematic Inversion. 20. Define Mechanical Advantage. It is defined as the ratio of the output force or torque, supplied by the driven link, to the input force or torque, required to be supplied to the driver link. 21. What is meant by planar mechanism? A planar mechanism is one in which all particles describe plane curves in space and all these curves lie in parallel planes: that is, the loci of all points are plane curves parallel to a single common plane. It utilizing only lower pairs is called planar linkages, they include only prismatic and revolute pairs. 22. What is meant by spatial mechanism? If there is any relative motion that is not in the same plane or in parallel planes, the mechanism is called spatial mechanism. Spatial mechanisms are three dimensional. 23. State the Property of Inversion Properties of Inversions: i) No of inversions possible for a kinematic chain equals the number of links in the parent kinematic chain. (ii) Relative motion (displacement, velocity and acceleration) between any two links does not change with inversion. This is simply because relative motion between different links is a property of parent kinematic chain. (iii) Absolute motion of points on various links (measured with respect to the frame-link) may, however, change drastically from one inversion to the other, even in direct inversion. 24. Define Sliding Connectors [Anna University, Nov 2013] When the two elements of a pair are connected in such a way that one can only slide relative to the other, then the connector is called Sliding connector. The piston and cylinder, cross-head and guides of a reciprocating steam engine, ram and its guides in shaper, tail stock on the lathe bed are examples of Sliding Connectors. 25. Differentiate Rotation and Translation [Anna University, Nov 2013] Translation: A body has translation if it moves so that all straight lines in the body move to parallel positions. Rectilinear translation is a motion where in all points of the body move in straight line paths [Eg. The slider in slider cranks mechanism]. Curvilinear translation is translation in which points in a body move along curved paths. [Eg. Tie rod connecting the wheels of a steam locomotive] Rotation: In rotation, all points in a body remain at fixed distances from a line which is perpendicular to the plane of rotation. The line is the axis of rotation and points in the body describes the circular paths about it [Link 4 – Rectilinear translation] [Link 3–Curvilinear translation&Links 2, 4 – Rotation] 26. Classify Constrained Motion [Anna University, June 2014] When the motion of a kinematic link/pair is restricted to a particular direction/path, it is called constrained motion. It can be classified as: (i) Completely Constrained Motion: If the movement of the link is restricted to move in one particular path only, it is completely constrained. (ii) Incompletely Constrained Motion: If the movement of the link is restricted to move in more than one path, it is incompletely constrained motion. (iii) Successfully constrained motion: If the movement of the link is restricted to one particular path and made it to stop at particular length of the movement it is successfully constrained motion PART B 1. Describe Whitworth's quick return mechanism with neat sketch. 2. Define inversion of mechanism. Explain the inversions of four bar mechanism with neat sketch with suitable example. (or) Sketch & explain any three kinematic inversion of 4 bar chain. [Anna University, June 2014] 3. Explain the various inversions of double slider crank mechanism with neat sketch. 4. Design a four-bar crank rocker quick return mechanism to give a time ratio of 1.25 with rocker swing angle as 75° clockwise. Assume the output link (rocker) length as 50 mm and in the right extreme position it is vertical. St.Joseph’s College of Engineering / St Joseph’s Institute of Technology Fig 1 ISO 9001: 2008 3 Fig 2

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ME6401-Kinematics of Machinery Mechanical Engineering 2014-2015 5. i) Explain the various inversions of single slider crank mechanism with neat sketches.  ii) Determine the degrees of freedom (Fig 1) for the following linkages  [Anna University, November 2013] 6. (i) Find the maximum and minimum transmission angles for the mechanisms shown in fig.2. The figure indicates the dimension in standard units of lengths. (8) (ii) Write short notes on toggle mechanism (8) [Anna University, November 2013] 7. Explain mechanical advantage and transmission angle related to four-bar mechanisms. 8. Illustrate a crank and slotted lever mechanism as an inversion of single slider crank chain. Deduce an expression for length of stroke in terms of link lengths. 9. State and prove Kutzbach criterion for the following kinematic chains: Three bar chain, Four bar chain, Cam with knife edge follower. 10.Sketch & describe the working of two different type of quick return mechanisms. Derive an expression for the ratio of time taken in forward & return stroke for one of these mechanisms. [Anna University, June 2014] 11. Sketch and explain any various types of straight-line motion generating mechanism. 12.Explain in detail about Universal Joint and derive an expression for maximum and minimum speeds for driven shaft and maximum fluctuation of speed. 13.(a) Explain about the double universal joint and its advantages over single joint with neat sketch. (8) (b) The angle between the axes of two shafts connected by Hooke’s joint is 18°. Determine the angle turned through by the driving shaft when the velocity ratio is maximum and unity. (8) UNIT – II KINEMATIC ANALYSIS PART A 1. How will you determine the direction of Coriolis component of acceleration? The direction of coriolis component of acceleration can be determined by rotating the velocity of sliding vector vs through 90˚ in the direction of rotating angular velocity . Direction of coriolis acceleration Normal acceleration 2. Explain normal component of acceleration. The acceleration of a particle at any instant moving along a circular path in a direction normal to the tangent at that instant and directed towards the centre of circular path [direction from A to O] is called normal component of acceleration or normal acceleration. It is also called as radial or centripetal acceleration. ‘ar’ – in the figure shows the normal component of acceleration for acceleration ‘a’ 3. Define rubbing velocity. [Anna University, December 2012] The links in a mechanism are mostly connected by means of pin joints. The rubbing velocity (Vr) is defined as the algebraic sum between the angular velocities (ω) of the two links which are connected by pin joints, multiplied by the radius(r) of the pin. Vr = ωr. 4. Define Corioli’s component of acceleration. What is the expression for Corioli's component of acceleration? [Anna University, June 2014] When a point on one link is sliding along another rotating link, such as in quick return motion mechanism, then the coriolis component of the acceleration must be calculated to determine the direction of acceleration component. It can be calculated by: 5. Define Instantaneous centre of rotation. [Anna University, June 2014] The combined motion of rotation and translation of the link may be assumed to be a motion of pure rotation about some centre I, known as the Instantaneous Centre of rotation. [Also called as Centro or Virtual centre]. In the figure, the link AB has4 a translatory (curvilinear) motion as well as rotary motion and moves to the position of A1B1 as shown. In instantaneous centre method it will be considered as a pure rotation about the centre I which is called Instantaneous centre. St.Joseph’s College of Engineering / St Joseph’s Institute of Technology ISO 9001: 2008