THEORY OF MACHINE
MECHANISM AND MACHINE Simple mechanisms:-Kinematics link or element:-Each part of the machine which is relative motion with to some other part will be known as Kinematics link or element. It is necessary for the link to be a resistant body. So that it is capable of transmitting power and motion from one element to the other element. TYPES of link:-1) Rigid link: - Deformation are negligible (microscopic) E.g. Cams, connecting Rod, piston, cylinder. 2) Flexible link: - Deformation are not negligible, but are in permissible limits, E. g. Belt, rope, chain drive. 3) Fluid link: - when the power is transmitted due to fluid power. E.g. Hydraulic breaks lift.
Different types of relative motion for, relative motion = system will be having two, links. 1) Completely constrained motion: - Desired motion 2) successfully constrained motion: - Given desired motion .Shaft in footstep bearing 3) incompletely constrains motion:-Indepently two motions are there perpendicular is rotation second is reciprocating Kinematic pair:-A connection between the two links is always known as joint or a pair. But these pair wills only a Kinematic pair. If the relative motion between a link a constrained motion. Rolling: - It is combination of translation and rotating Pure rolling: - Rolling without any kind of slipping.
Classification of kinematics pairs:- (a) According to the type of relative motion:-Turning pair ( Rotating pair ) ( pin-joint ) When the relative motion is pure turning Sliding pair ( prismatic pair )When the relative motion is pure sliding. E.g. Key in key-way. Rolling pair:-When the relative motion between two pair is a pure rolling. (Rolling without slipping) Screw pair: - When the relative motion is over the threads. For Ex. Nut and bolts. Higher pair is equivalent to two lower pair.For eliminate the perpendicular pair 1 link is required Spherical pair :- ( Ball in socket joint ) When the relative motion between two links are the 3-D rotation ( spherical motion) 3) According to type of contact :-Lower pair :- surface contact, Higher pair :- point or line contact, Wrapping pair :- Multiple point contact When one link is wrapped over the other link For Example :- Belt and pulley , Rope - pulley , chain and approve 1 higher pair = 2 lower pair. C) According to the type of closure:-Self closed or closed pair: - Those pair which are hauling permanent contact. Ex. Turning, sliding Opened pair or Forced closed pair :- Those pair which are having forced contact Ex. 1) Higher pair in cam and follower 2) Doors closer 3) Automatic clutch operating system:-
Different Types of pairs or joint:-Binary joint :- ( lower pair is in form binary joint) Where two links are connected. Ternary joint: - Where three links are connected at one joint .Quaternary joint:-where four links are to be connected. Kinematics chain: - If all the links are connected are in such way that the first link is connected to the last link in order to have close chain and if all the relative motion in this close chain are constrained then such a chain is known as Kinematics chain or constrained chain. To used this chain one link must be fixed Degree of reed's :- ( mobility) The minimum number of independent variables to required to define the position or motion of the system is known as degree of freedom of the system.
Restraints: - number of those motion which as not possible and are to block Restraints are always due to pairs. Aim: - To find out the D. O. F. Of (2-D) Plane mechanisms L= number of links in mechanical j = number of binary joint. The DOF of cam and follower is always 1 For any followers. Unconstrained chain :-DOF is the number of inputs required to get constrained output in any chain Spring as a link :- A link of flexible length Grublers equation :- For those mechanism in which First mechanism in history of lower pair Simple mechanism ;-Four bar mechanism Single slider Double slider The first mechanism mass be made by 3- link ( cam and follow ) But without any higher pair the first mechanism is and bar chain mechanism Four bar mechanism :-( quadric cycle mechanism ) Best position :- Fixed position - because it governs both input and output links Worst position - coupler
INVERSION (Mechanical which are obtained by fixed one by one different links) Double crank, Crank -Rocker, Double - Rocker VERY IMPORTANT GRASHOFS LAW:- For the continuous relative motion between the number of links in four bar mechanism the summation of the length of shortest and longest length should not be greater than the summation of the length of other two length. For continuous relative motion , S +l <= P + q Best position -- Fixed input or output Best link for complete rotation -- shortest length link S + l = p + q law satisfied . S- Fixed = Double crank adjacent to fixed = crank --Rocker s- coupler = Double rocker If s + l = p + q law satisfied Not moving pair of equal links 2=s 5= l 4=p 3= q Same as previous If s +l = p + q law satisfied Have the pair of equal link 2=s 2=s 5=l 5=l
1) parallelogram linkage or ( Golden linkage ) :-S-fixed = Double crank L-Fixed = Double crank 2) Deltoid linkage :-S-Fixed = Double crank, L-Fixed = Crank - Rocker Note:- If s + l > p + q Law is not satisfied Any link fixed Double- Rocker Some practical application of 4- Bar mechanism 1}Beam engine mechanism ( SIR JAMES WATT ):-Rotation = oscillation Crank = Rocker 2) coupling rod of locomotive :-Rotation = rotation Transmission angle :-The angle between the coupler link and output link in four bar mechanism is known as transmission angle.
Single slider crank mechanism :- (Drag and link mechanism ) 4 link + 3 turning pair+1slidingpair 1st inversion = In this cylinder is fixed and it is basic inversion 1st inversion cylinder is fixed, Rotation = Reciprocation, Crank = piston , Output = input = Reciprocating engine, Input = output = reciprocating compressor, Crank fixed :-2nd inversion 1} With worth quick return motion mechanism 2} Rotary IC engine mechanism ( Gnone Engine ) C. R. FIXED:-3RD INVERSION Crank and looted lever mechanism Oscillating cylinder engine mechanism Slider fixed 4rth INVERSION hand pump ( pendulum pump ) Bull engine Crank and slotted lever QRMMC connecting Rod is fixed
With worth QRMM :-2nd inversion ( Crank fixed ) In this, rotation = Rotation ( Crank fixed ) In this , Rotation = Rotation (Double Crank ) Stroke = R1 R2 = C1 C2= 2(OC ) ( only this length it is dependent ) Rotary ic engine (Gnone engine ) :-2nd Inversion ( Crank is fixed ) When combustion takes place inside the cylinder Input force comes on the piston This force is transmitted to CR and piston both rotation Cylinder block rotates ( output ) Hand pump ( pendulum pump or Bull engine ) :-4rth inversion in this slider or piston is fixed DOUBLE SLIDER CRANK CHAIN :-4 Link + 2 Turning pair + 2 sliding pair 1) slotted plate is fixed :- ( elliptical Trammel ):- 2. IF any of the slider is fixed:-Scotch yoke mechanism Rotation == Reciprocating
3) If the connecting slider is fixed Oldham’s coupling This is used to connect the shaft having lateral misalignment Maximum sliding velocity of slotted plate = ( Distance between the shaft ) x W driver Very imp MECHANICAL ADVANTAGE OF A MECHANISM :-Toggle Mechanism :-Force output is very higher than force input. Toggle position in 4 bar mechanism :-Extreme position of output link are Rocker in 4- bar mechanism A) left extreme position of output link B) Right extreme position of output link Starring gear mechanism :-Changing the direction of motion 1) Ackerman’s Starring mechanism Hacking only turning pair Life is only high Only exact at three position MID position Two extreme position 2) Daulis Starring mechanism Best but not in used because life is very less Hauling turning pair and sliding pair Life is very less Exact at all position 3) Rapsons slide :- (3D mechanism) Cross slider mechanism Used in ships (when high radius of curvature) Intermittent motion mechanism Periodic motion with constant breaks output with respect to given continuous input. 1)
2) Ratchet Mechanism
Straight line motion mechanism :-( extension of simple mechanism ) A) Exact straight line motion mechanism B) Approx straight line motion mechanism For example :-Hart's mechanism = 6 link, 4link, Tchebosoffs mechanism, Grass hopper mechanism, Scotl – Russell mechanism, Modified Russell mechanism, Robert's mechanism, Pontograph. Watts indicator mechanism :-Watts indicator mechanism Imp Observation There is no relative motion between link BC and CD BCD ---->one link Point C and point Q both move in approx St line motion (Approx St. Line motion mechanism ) LINK BCD & LINK AQ= lever , Rocker Double lever mechanism An alternative was to check the chain :-If (j+h/2) = (3/2 L -2 ) ----kinematic chain If, (j + h/2 ) > (3/2 L -2 ) ----frame / structure /superstructure If different of LHS and RHS = 0.5= Frame / structure If different of LHS and RHS > 0.5= superstructure If , ( j + h/2 ) < ( 3/2L -2 ) -----Unconstrained chain