1.1 : Kinematics of Machines
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1 1.1 : Kinematics of Machines Q.1.Define Statics, Dynamics, Kinetics and kinematics. Ans: Statics :- It is the branch of engineering which deals with study of forces and its effect on bodies at rest. Dynamics :- It is the branch of engineering which deals with the study of forces and its effect on bodies in motion. Kinetics :- It is the branch of dynamics which deals with study of forces and their effect on bodies in motion considering mass of the body. Kinematics :- It is the branch of dynamics which deals with the study of forces and their effect on bodies in motion without considering mass Q.2.Define Kinematic link,kinematic pair, Kinematic chain,mechanism & inversion a ] Kinematic link ( or element ) : It is defined as a resistant body which has relative motion with some other element. e.g. crank, Piston, cylinder, frame b] Kinematic pair : When two links are connected in such a manner that relative motion between them take place in a definite way then it is called kinematic pair. c] Kinematic chain : When two or more kinematic pairs are joined together, they form kinematic chain. d] Mechanism : If one link of a kinematic chain is fixed it is called mechanism. e] Inversion : When different links of chain are fixed we get different mechanisms, these mechanisms are called inversions of that kinematic chain. The number of inversions of a kinematic chain is equal to number of links in that chain Q.3. Classify kinematic link. Or What are the types of links? Ans. Types of links 1. Rigid link e.g. connecting rod, lever. 2. Flexible link e.g. chain, belt rope etc. 3.Fluid link e.g. oil in hydraulic system,air in pneumatic system 4.Types of Links based on attachment. a] Binary link - Having two connection b] Ternary link - Having three connections c] Quaternary link - Having four connection
2 Q.4.Differentiate Between Structure and Machine Q.5.Differentiate Between Machine and Mechanism
3 Q.6.State Different types of pairs and explain with sketch. Ans : A) Kinematic pairs according to the relative motion Sliding pair: When relative motion between two elements of a pair takes place in the form of SLIDING, then the pair is called sliding pair. example, a rectangular bar in a rectangular hole, the piston and cylinder of an engine, the cross-head and guides of a steam engine, the ram and its guides of a steam engine, the ram and its guides in a shaper, the tailstock on the lathe bed etc. Turning pair: When relative motion between two elements of a pair takes place in the form of pure TURNING only, then the pair is called turning pair. for example, a shaft with a collar at both ends revolving in a circular hole. The collars prevent the sliding motion of the shaft in the bearing.
4 Rolling pairs: When two elements are so connected that one is constrained to roll on another element which is fixed, they from a rolling pair. Example Ball and roller bearings, a wheel rolling on a flat surface etc. are examples of rolling pairs. Screw (or helical) pair: When one element turns about the other element by means of threads, they form a screw pair. The motion in this case is a combination of sliding and turning. Example the lead screw of a lathe with a nut, a bolt with a nut, Screw and nut of screw jack are some examples of screw pairs. Spherical pair: When one element in the form of sphere turns about the other element which is fixed the form a spherical pair. Example-the ball and socket joint, a pen stand, the mirror attachment of vehicles etc, are some examples of spherical pairs.
5 B) Kinematic pairs according to the type of contact. Lower pair: When the two elements of a pair have surface(area) contact while in motion the pair is called a lower pair. All sliding pairs, turning pairs and screw pairs form lower pair. for example, a nut turning on a screw, a shaft rotating in a bearing, an universal joint, all pairs of a slider crank mechanism, a pantograph etc. Higher pair: When the two elements have point or line contact while in motion then the pair is known as higher pair. Belt, rope and chain drives, gears, the cam and follower ball and roller bearings, a wheel rolling on a surface etc all etc. All form higher pairs. C) Kinematic pairs according to the type of mechanical constraint Closed pair: When the two elements of pair are held together mechanically in such a manner the only the required type of relative motion occurs, they are called a close pair. All lower pairs and some higher pairs (for example, the enclosed cam and follower) are closed pairs. Unclosed pair: When the two elements of a pair are not held mechanically and are held in contact by the action of external forces, the pair is called an unclosed pair. for example, the can and spring loaded follower pair Use of Pairs in robots
6 Q.7. What do you mean by constrained motion? What are types of constrained motion. Ans: 1) Incompletely constrained motion: When the motion between a pair can take place in more than direction, it is said to be incompletely constrained motion. For example, a circular shaft revolving in a circular hole. 2) Completely constrained motion: When the motion between a pair can take place in one and only one way, it is said to be completely constrained motion For example, a rectangular shaft revolving in a rectangular hole. 3) Partially (or successfully) constrained motions: When the constrained motion between a pair is not completed by itself but by some other means, it is said to be partially constrained motion. The motion of shaft in a footstep bearing is successfully a constrained motion when compressive load is applied to the shaft Q.8. What are different types of Kinematic Chains? Ans: The various type of kinematic chain are 1. Four bar chain or quadric cycle chain 2. Single slider crank chain 3. Double slider crank chain
7 1.2 : Inversions of Kinematic chains Q.1.Enlist various Inversion of three types of Kinematic chains?
8 1.3 : Inversions of Four bar chain or Quadratic cycle chain Q.1.Explain the coupled wheels of locomotive mechanism. Ans. Links - links AD frame (Fixed) link AB (Crank) link BC (Coupling Rod) link CD (Crank) Pairs - Turning Pair = AD (Frame) & AD (Crank) Turning Pair = AD (Frame) & CD (Crank) Turning Pair = AB (Crank) & BC (Connecting Rod) Turning Pair = CD (Crank) & BC (Connecting Rod) Construction: This mechanism is an inversion four bar kinematic chain. This has four turning pairs. It is consists of frame AD which is fixed, on which two cranks AC & BD are fitted on it.the cranks are free to rotate about points A and D. Both the cranks have same lengths. Two cranks are connected to each other by means of coupling rod, Connecting the other ends B and C of both cranks. At the connections B and C there is turning pair. Working When link AB starts rotating about fixed point A. The rotary motion of wheel is transmitted to next wheel by means of coupling rod BC. As a result the other wheel also starts rotating in same direction and same speed, because both cranks have same radius of rotation. Application The mechanism is used to connect driving & driven shaft of locomotive. Here both driving & driven wheel must rotate in same direction
9 Q.2. Explain with sketch Beam engine Ans. links - Link 4 OC (frame) Link 1 OA (Crank) Link 2 AB (connecting Rod) Link 3 BCD (lever) Pairs - Turning Pair = Frame OC & Crank OA Turning Pair = Crank OA & Connecting Rod AB Turning Pair = Connecting Rod AB & lever BCD Turning Pair = Frame OC & lever BCD Construction This mechanism is an inversion of four bar chain. It has four turning pair. It consists of frame OC which is fixed and on which all other elements are fitted. The Crank is fixed at pt. 'O' at frame. The crank is free rotates about pt.'o'. Other end of crank is connected to connected rod AB. Other end of connecting Rod AB is linked to one end of lever. The lever is pivoted at pt 'C' other end of lever 'D' is attached to piston -cylinder mechanism as shown. Working As the crank starts rotating this motion is transmitted to lever by connection rod. As crank continues to rotate the lever starts to oscillate about pt. 'C', this oscillatory motion is transmitted to piston & cylinder. Application The mechanism converts rotary motion to reciprocating motion. This is used in machine tools & pumps. It is used for extracting oil from oil wells, the equipment is called pumpjack
10 Q.3.Explain with Sketch Pantograph Links Link AB - End A is fixed link BC link DE link DF Pairs - Turning Pair - AB & BC Turning Pair AB & DE Turning Pair BC & DF Turning Pair CD & AD Construction This mechanism is an inversion of four bar chain. It has four turning pairs. One link is fixed to the table. The stylus is attached to the junction of link DE and DF and the pen is attached to the end C of the link BC. The lengths of all links are adjustable through the holes provided on the links. Working As the operator traces the "Drawing" with the stylus, the same drawing is reproduced by the pen either in enlarged or reduced scale depending upon the links lengths. The links have holes for the adjustment of magnitude of enlargement or reduction. Application The mechanism is used for 1. Reducing large drawing. 2.Used in copy machining such as copying lathe using hydraulic system. 3.Used in electric train supply system on top of train, which supplies current to electric train from cables on top
11 1.4 : Inversions of Single slider crank chain Q.1. Draw the basic single silder crank chain and explain how different inversions are obtained by fixing different links. Ans: Basic structure of single slide crank chain is shown below FIXED LINK Frame fixed Crank Fixed Applications of inversion Basic singl silder mechanism Gnome engine Whit-worths Quick return mechanism Connecting rod Fixed Oscillating cylinder mechanism Crank and slotted lever quick return mechanism Slider fixed Pendulum pump
12 Q.2.Explain with Sketch Oscillating Cylinder Mechanism. links - Crank- Connecting Rod & piston {both form one link} Cylinder Frame {Fixed} Pairs - Turning Frame & Crank. Turning Crank & Connected Rod & Piston. Sliding Piston & Cylinder. Turning Frame & Cylinder. Construction This mechanism is an inversion of Single slider Crank Chain.It has three turning pairs & one Sliding pair. As shown in figure. both connecting rod & piston form one link. There is no relative motion between connecting Rod & Piston. The cylinder is pivoted to frame, due to which whole cylinder is free to oscillate about the frame. Working When crank starts rotating, it causes the piston to reciprocate inside the cylinder. A piston while reciprocating causes the cylinder oscillate about pt.'o',because there is no relative motion between connecting rod and piston. Application The mechanism is used where rotary transmitted into oscillating motion. It is used in printing press m/c
13 Q.3.State and explain Bull engine mechanism {Pendulum Pump} Links - Crank Cylinder Piston & Piston Rod Connecting Rod. Pairs- Turning Piston & Piston Rod & Connecting Rod Turning Connected Rod & Crank Sliding Piston - Piston Rod & Cylinder. Turning Crank & Cylinder. Construction This mechanism is an inversion of Single slider Crank Chain.It has three turning pairs & one Sliding pair. As shown in figure the first link is piston and piston rod, second is connecting rod which is extended beyond its connection to crank. the third link is crank and fourth link is cylinder which is placed vertically and is fixed. Working When the upward motion is given to connected Rod it causes downward motion of piston & vice versa. Application The mechanism is used in duplex pump in boilers, and also in manual hand pumps fitted on bore well
14 Q.4. Explain with sketch Gnome Engine or Rotary Engine Links - 1.Crank (fixed ) 2.Piston 3.Connecting Rod 4.Cylinder & Frame Pairs- Crank & Connecting Rod turning Connected Rod & Frame turning Crank & Frame turning Piston & cylinder - Sliding Construction This mechanism is an inversion of Single slider Crank Chain.It has three turning pairs & one Sliding pair.as shown in diagram it has 5 or 7 cylinders and connecting rods of all pistons are connected to one point which is another end of crank. In this mechanism crank itself is fixed. Working As pistons start reciprocating inside cylinders, whole frame starts rotating about fixed pt 'O' the crank remains at its place. The rotation of frame causes suction, comp,expansion & exhaust strokes in different cylinders at same time. Application It was used in airplane engines
15 Q.5. Explain with sketch Crank and Slotted lever quick mechanism used in shaping machine. Ans: Links - 1.Slider 2. Crank 3.Frame 4.Slotted Lever Pairs- Frame & Slotted lever turning Frame & Crank turning Crank & Slider turning Slider & Slotted lever - Sliding Construction This mechanism is inversion of Single slider Crank Chain.It has three turning pair & one Sliding pair. Crank is fitted to frame at pt.'a' & slotted lever is fitted to frame at pt.'b'. The crank & slotted lever are connected to each other through slider. The slider is free to slide in side slotted lever. The upper end of slotted lever is attached to the ram of shaping machine through a linkage {The ram and lever connecting to ram are not part of the basic inversion} Working As the crank starts rotating about pt.'a', it also transmits motion to slider. As the slider is fitted inside the slotted lever, the slotted lever starts oscillating about pt.'b'. As shown in second fig. The forward stroke is making an angle of θ, Whereas the return stroke covers and angle of β. From the figure it is clear that angle θ > β, hence forward stroke is takes more time than return stroke. Hence this mechanism is called as quick Return mechanism. Application The mechanism is used in shaping machine
16 Q.6. Explain with sketch Whitworth s quick return Mechanism? Ans: Links: Crank BC Slotted lever EAD Slider Frame AB (FIXED) {Link Es is not part of basic mechanism} Pairs: Crank BC and frame AB : Turning Pair Slotted lever EAD and frame AB : Turning Pair Crank Bc and slider : Turning Pair Slider and Slotted lever EAD : Sliding pair Construction : This mechanism is an inversion of single slider crank chain. It has three turning pairs and one sliding pair. It has crank BC turning about point B. Other end of crank carries a slider, connected with turning pair. The slide fits inside the slotted lever EAD. The slider is free to slide inside the slotted lever. The lever is pivoted at point A. The lever rotates about the point A. End E of this lever is connected to the Ram of the shaper machine. Working: As the crank starts rotating about the point B. It transmits the motion to the Lever EAD through the slider. As a result the lever EAD starts rotating about the point A. As shown in figure the forward stroke of the ram is slower and return stroke is faster ( Angle theta is greater than angle beta). Hence this mechanism is called quick return mechanism. Application : This mechanism is used in Shaping machine
17 1.5 : Inversions of Double slider crank chain Q.1. Draw Basic double slider crank chain and explain how different inversions are obtained from it? Ans:Basic Double slider crank chain is shown below, It has two truning and two sliding pairs Various Inversions :
18 Q.2. Explain with sketch Scotch Yoke Mechanism? Ans: Links: 1.Frame (fixed ) 2.Crank 3.Slider 4. Yoke Pairs - 1.Frame & Crank turning 2.Crank & Slider turning 3.Yoke & Slider Sliding 4.Frame & Yoke - Sliding Construction This mechanism is inversion of Single slider Crank Chain.It has two turning pair & two Sliding pair. As shown in fig. The crank is fitted to frame at pt 'O'.A slider is attack to other end of crank at pt 'B'. The slider fits inside Yoke. A Yoke is free to slide inside frame. Working As the crank starts rotating about pt.'o' it causes the slider to slide inside Yoke. As the crank changes it's position it pulls or pushes the Yoke. Thus Rotary motion of crank is converted into Reciprocating motion of Yoke. Application This mechanism is used to convert Rotary motion into reciprocating motion
19 Q.3. Explain with sketch Oldham s Coupling Ans: Links: Frame (fixed) Shaft & Flange 1 Shaft & Flange 2 Intermediate piece. Pairs: Frame & Shaft 1 turning pair Frame & Shaft 2 turning pair Flange 1 & Intermediate piece Sliding pair Flange & Intermediate piece - Sliding pair Construction : This mechanism is inversion of Double slider Crank Chain.It has two turning & two Sliding pair. Two flanges with respective shafts are free to rotates with respect to frame both flanges have rectangular slots. An intermediate piece has two rectangular projections on both sides, both projections are perpendicular to each other, each projection fits inside the slot of flange. Working: When one shaft is given rotary motion,it is transmitted to another shaft the intermediate piece. The intermediate piece slides & adjusts itself, to keep both shafts runnings. The centre of the intermediate piece traces the path of a circle with radius equal to offset between shafts. Application : This coupling is used to connect two shaft having some eccentricity (offset)
20 Q.4. Explain with sketch Elliptical Trammel Mechanism? Ans: Links: 1. Frame 2.PB 3.Slider 1 4.Slider 2 Pairs: 1.Slider 1 & Frame Sliding 2. Slider 2 & Frame Sliding 3.Slider 1 & link PB turning 4.Slider 2 & link PB - turning Construction : This mechanism is an inversion of Double slider crank Chain.It has two sliding & two turning pairs. As shown in figure it has rectangular frame with vertical and horizontal slots. Two sliders are free to slide inside both slots. A link PB connects two sliders. Working: When one of the slider is given reciprocating motion it is transmitted to another slider through the link PB. It is observed that while the two sliders slide into respective slots the pt.'p' traces the path of an ellipse. Application : This mechanism is used for drawing ellipse of required size
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