Lecture 31

[Music] [Music] welcome to the next lecture on linkages and mechanisms this is a very important topic when we discuss through this entire course machines are supposed to do a particular task or multiple tasks in a machine you will have a structure then you will have a mechanism what is mechanism mechanism is the heart of a machine and when you talk about mechanism there is a component called linkage or links so that is what is the link between linkages mechanism and machines when we try to look into any machines you will have structure then you will have mechanisms the structure when you talk in civil engineering terms can be the frame on which the building is constructed when you talk about your bus a frame on which the bus is constructed for for example you will have a frame and then on the frame you put all the stainless steel material and cover the bus so that is the base structure the skeleton is called as a frame and when you raise highrise buildings again it is the structure so you can have structures and then inside the structure you can have mechanisms when you look at a cycle the frame whatever you have like a triangle is a structure and the chain where you have is a mechanism in this lecture we will try to have an introduction then introduction to linkages mechanisms four bar linkages kinematic pair kinematic chain and then we will try to see various mechanisms like quick return mechanism Cam and follow mechanism inversion of a mechanism then few real world examples and then finally we will try to have a recap linkages linkages are the fundamental components in mechanical systems that connects different parts to transfer motion and force two components are involved one is motion transfer the other one is force transfer two important things are there a linkages is used to transfer motion and forces linkages can be as simple as a lever to as complex as a multibar linkage used in a robotic arm robotic arm is like your hand which has a movement and you will have all this hand has lot of linkages and these linkages has to be moved and and when we try to carry a weight it also has a force right so if you see here there is a crank this crank moves like a lever this crank is in turn attached to your link from here let us keep it as link one then joint one so link two so your crank is attached to your link two then link one and Link two are joined together at joint one so now when the crank moves like this you will see there will be a motion which goes up and down there'll be a motion which goes up and down so let us look into mechanisms mechanisms are Assemblies of linkage that are designed to perform a specific function within a mechanical system this is what I said machine mechanism linkage or linkage mechanism machine okay when we talk about machine tractor is a machine then we have your cycle where in which your health cycle is a machine bus is a machine car is a machine a drilling machine is a machine so these are all machines which will have a structure mechanisms right uh so application in engineering uh is the linkages and mechanisms are essential in many engineering fields in automobile particularly uh they are used in suspension systems and steering linkages all these things which you make from your Lego kit will have gears then you'll have a frame then you'll have a tool which moves up and down all these things are called as mechanisms which tries to move the toy here in which there is no gears but you will have linkages when you pull a leg so you can see the bones moving and the lion or the uh leopard Galloping you can see that when you look at this mechanism whatever is there slider crank so you see here there is a link this is a link so you have a joint here joint here J1 J2 link one link two now this link is attached to an output whatever it is so it is attached to a pist which slides inside a cylinder if you look into it it is a typical automobile application you will have a spark plug here which tries to excite the flu air fuel mixture so inside which there is a combustion this combustion tries to exert pressure so this pressure moves the Piston up and down when the Piston moves up and down this piston will try is attached to your joint and this joint will move the link back and forth when the link moves you can transfer it to the wheel or it can go VC Vera okay so the mechanisms are very important in this lecture our learning objectives will be understand the basic concept grasp the principles of linkage and mechanism including their geometry motion and force transmission as I told you mechanism will have two things one is force the other one is motion you can have only motion only Force you can have a combination of this we will also analyze the simple mechanisms learn to evaluate the motion and force characteristics of simple mechanisms and calculate input output relationship so here we apply Concepts to Real World Systems use linkages and mechanism principle in Practical mechanical design selecting and designing systems to meet specific functional requirement so you can see the Ratched wheel mechanism is used here this is Paul so Paul is spring loaded so that means to say every time when you move there is one click so it stops with one teeth motion when you try to go in the opposite direction you can press the pole and the rat head can rotate see this is a self loocking mechanism so if you go in the inverse Direction you can see there will be a slipping happening that's why in bicycles when you go in the forward Direction you will see there will is a transmission of motion when we go reverse Direction there will be a cluck clck cluck clck cluck sound so that is nothing but Ratched and Paul mechanism it is there and linkages if you see joints links are there when we try to pull one here you can try to have some motion like your sector getting cleaned a wiper which is getting moved this is your closed one this is a open one so and again interestingly what you have to Define in the link you will have to define the length and when you make a joint then you will have to make a Theta there so this is Theta what angle does the link move with respect to the Joint linkages are Assemblies of rigid bodies known as link connected by joints to form either a closed chain or a series of closed chain can be one closed chain it can be series of closed chain there are designed to transfer motion and force within mechanical systems so what are links and Joints links are nothing but a rigid component in a linkage that moves or remains stationary relative to each other is nothing but a link so this is link this is link this is a joint this is a joint and this is a joint right it can be in linear fashion it can also be in sector Arc fashion that means to say you make a slot or you push this then this will move an output so here it is only a segment which is used so here it is finite position you can also have a slot to vary and have infinite the uh vertical movement whatever it is so if you look into other mechanisms like your crane Crusher is also a mechanism your staircase climbing Robo is a mechanism you have some mechanism inside that also decides it and then you want to move in your health lab or in your Fitness room you would like to have a structure which goes up and down that is also a mechanism so you see a mechanism can be used at multiple places first let us try to understand what is four bar linkage so in four bar linkage you will have linkages that consist four links four links connected to four re revolute joints which are widely used in mechanical systems for tasks such as motion transmission and amplification so link one two three and then ground link four so you have a fixed link then you have pivots which are attached to it then each link you will be attached to a joint and here you move L2 and then you will try to have a motion in L2 which is connecting L3 also linkages have not come into existence now they have a long history with early development in mechanisms traced back to ancient civilization mechanisms have been there so in fact the mechanisms of throwing bombs or throwing heavy weight on the opponent during a war also has a mechanism springloaded they put a very heavy steel ball they hit hammer it and then that travels in a projectile motion to to hit at the neighbors and opening and closing of the Kingdom's door right when you go to many of the forts you see a very massive structur door so that will be in turn moved or uh reciprocated uh in a swinging action or in a sliding action there also we use mechanisms when you visit any of the big temples you will see Heavy doors which needs at least six seven people to open and close there also they have these mechanisms so it has a long history right they became crucial during the Industrial Revolution enabling the creation of complex machines like steam engine their evolution have significantly impacted modern engineering particularly robotics automobile and Machinery so when we talk about linkages there are types of linkages what are the types one it is only planar Motion in a plane it moves up and down it rotates it wipes it slides in a plane so the other way is in a space see I and earlier I moved it in a plane wiper of a car in a plane now I am using a robotic arm to clean the floor so I clean it in an arc for in XY I try to clean and also I move in Z Direction so threedimensional so you can have planar linkage spatial linkage all the components which move in parallel planes with motion confined to two dimensions are pler linkages wiper of a car wiper which is is used for cleaning the pan or some reciprocating motion you want in a plane spatial linkages are linkages which operate in threedimensional allowing movement in multiple planes example robotic arm aircraft landing gear mechanism aircraft landing gear is also a typical mechanism it's a mechanism which we generally discuss in length in mechanical engineering open chain linkage uh and closed chain linkage open chain linkage they do not form a loop and have free ends like I move my hand free hands they are more flexible and are used in systems like cranes and roboteam so this is one type this is other type so you'll have a closed one before we move to closed one let us see some examples uh where the spatial linkages in Car steering we have spatial linkage ages right robotic arm we have spatial linkages so here if you look at it in a plane you have a reciprocating motion so it is in a plane you will have your um motion so this is your planar linkage when we try to talk about closed linkage they form a loop where each link is connected to another link these are more rigid commonly used in mechanisms like bicycle and engine so if you look at it this is a stward platform which is exhaustively used in robotic arm and machining there are other applications but in Machining also it is trying to do what is the best part of it so here you have a polar coordinate system to control or in in cartisian coordinate also you see that X y z motion of the uh arms here it is controlled hydraulically or pneumatically so they are all independent and they can all be precisely controlled so uh the examples of planar open chain is pendulum system in a clock then planar closed link is a four bar mechanism used in automobile suspension spatial opening chain is in the robotic arm we have already discussed spatial closed is a stward platform which is used in flight simulators everywhere they use these uh examples so different types of uh mechanisms what are the different types of mechanisms there are many but I'm just giving you some of the examples in fact the sissor lift which is used in cranes when you see in construction industry that is also a link C mechanism is used which is used in airports from the ground level to lift all the food items or other necessary items or to move a stretcher from a plane to a ground level we use a scissor lift that is also a mechanism so some of the types of mechanisms are one is reverse motion linkage you can have so in Reverse motion linkage you will have a PIV here and then you will move this so you can move this right this is a reverse motion these are all links and here is a joint so B you can try to have Push Pull It is left to your smartness how do you use which linkage or mechanisms so here if you see it will be so here is a joint here is a joint here is a joint joint and here this can move and again this can move so here you will have a you are having fixed the third one is you can have parallel motion linkage in parallel motion linkage let me draw the linkage itself so that you can understand so these are all the joints so it can move this you can move this way that way you can keep moving so here is a moving part okay so if you want to convert this also into a linkage so it will be something like this you will have a link we will have a link so here this is motion here this is moving part so this will be your moving part in the similar way you can also have for this the D type which I was interested to show you is Bell crank linkage where in which you will have a link then you can have a mechanism which goes like this so here if we try to move this so this is a fixed joint so you will have so here it is a fixed pivot and here it is the moving this is moving so these are some of the moving part these are some of the uh mechanisms or linkages uh which I thought I will give you and based on each of them they have examples now let us understand four bar mechanism in a four bar mechanism you will have a frame which is at the base then you will have a driver which drives the entire circuit you will have a coupler which links between these two coupler then you will have a follow over based on this motion you will try to see the a moving up and down it's a simple mechanism consisting of four rigid connected by four joints it is one of the most fundamental and widely used mechanisms in mechanical engineering so the components whatever we have is a ground which is fixed the stationary link to which all other links are connected is called as the ground or it is called as the base next we have a crank crank is a place where we used to give an input so this is called as crank so crank the rotating link that drives the motion uh of the mechanism it is connected to the ground and usually provides an input motion for example if you see this wheel is a crank then you have a coupler which is nothing but a connecting I have already told you three so the linkage that connects the crank and the follower where is a follower uh lello is a follow a or four is a follow so the linkage that connects the crank and the follower it transfers motion and force between the input and output and the last one is going to be the follower which is nothing but the output what is a follower the yellow link is a follower follow over is the link that is driven by coupler it produces the desired output motion I would like to repeat coupler later we will see cou which is a connecting link connecting link link is is three connecting link is three so the link that connects the crank and the follower which transfers the motion and force uh between the input and output so this is the base is called as a frame this is called as a crank this is called as a connecting rod and this is called as a rocker so now once this is done the next important thing is degrees of freedom so degrees of freedom of your four bar linkage are determined by the number of independent movements possible within the mechanism so how many different motions it can have independently is is what is degrees of freedom for a planar four bar linkage the degree of freedom is typically one meaning that if the input link moves the position of all other links are fully determined okay in links there are different types one is called as a binary link binary link means one with two notes so I will have a link this is a link this is called as binary link and what are these These are called the nodes you can have tary links here you will have one with three nodes it's like a triangle this is turn right you can have three is quinary link so what is quinary one with with four nodes which are something like this your links need not be always binary it can be tary it can be also quinary and why is this links talked more is because when we talk about degrees of freedom and motion getting transferred we we always look forward for the correct possible links so now let us try to solve a simple problem with so binary links can be represented like this tary links by a triangle you will have a notes quattra right the other one you can also have something called as grounded joints grounded half joints these are grounded half joints okay so you can have uh many more things so we can have a moving rotating joint so it is grounded half joint if you just represent it by a circle it is called as moving rotating joint then you can have grounded you can have grounded I said half here you can also have grounded full joint or grounded rotated joint rotating joint you can have this so these are all different joints uh which are there so that basically the links can add and then give a motion to it okay now let us try to figure out degrees of freedom in degrees of freedom as I told you independent motion which can happen you can have a structure which is a super structure or a structure with degrees of freedom what are super structures definitely you have to give a drive to that mechanism so that the entire mechan mechm can move or it is such a rigid one where Drive externally has to be given so those mechanisms are called as super structure mechanisms or super structure when you try to figure out degrees of freedom the gluers equation the gluers equation is used to calculate the degrees of freedom for planar mechanism which is degrees of freedom is equal to 3 n -1 - 2 J 1 minus J2 the number of links J1 is number of degrees of freedom joint and J2 is for number of two degrees of freedom joints on a higher pair so for a four bar mechanism you try to get degrees of freedom as one this confirms that the four bar mechanism has one degree of Freedom making it a single input mechanism that means to say you drive one input so that you get the output whatever it is output can be sweeping or windshield cleaning so explanation and application uh to four bar mechanisms GL gluers equation show that four bar linkage the motion of one link controls the motion of the entire mechanism this property makes four bar linkage suitable for various applications in engine robotic arm and various Machinery it is also used for precision motion control what are the different types of motion you can try to have with the four bar mechanism you can try to have your rotational motion an oscillatory motion a translation motion rotation motion you can see that there is a crank which rotates there is a connecting rod which connects between this and then you have a link which is a fixed and then an oscillating motion so rotating motion oscillating motion some linkages May exhibit oscillatory motion pendulum clock where they rotate back and forth over a limited angle pendulum clock or a segment the motion is commonly observed in the follower or coupler when they are constrained by a linkage geometry translation motion translation is sliding uh although less common in basic fourar linkage certain configuration or extensions can produce translation motion where the links move in a straight line so moving further in kinematic pairs mechanisms can be considered as a kinematic chain assembled from elementary kinematic pairs formed by two rigid bodies in direct contact the analysis of mechanisms depend on studying these kinematic Pairs and their specific relative motion they allow between the two interconnecting rigid bodies so kinematic we know we are now seeing kinematics pair there are two classifications lower order kinematic pair and a higher order kinematic pair in a lower order kinematic pair these occurs when the connection between the two bodies is realized through a surface of contact maintained between them they are one of the two main classes of kinematic pair the higher order is this involve contact between the lines or points of the two bodies they are called as the higher kinematic pair so the chematic chain assembled for elementary kinematic pair formed by two rigid bodies in direct contact one is surface contact another one is line or Point contact so at types of kinematic pairs you can have revolute joints or rotary joints the figure is given here uh the relative motion between the two connected bodies is purely rotation which is used in hinge of a door or in joint of a robo you can have Prismatic joints which are nothing but sliding joints it permits linear motion along a single axis allowing one body to slide on the other the like a drawer which is used in the table or a linear actuator falls under Prismatic joints you can have cylindrical joints where they allow a rotation motion and a translation so you see a translation and a rotation which is exhaustively used in Robos which is used in piston moving within a cylinder or telescopic shafts spherical joints ball and socket joint ball and socket joint is there in your hip and in your arm permits rotation motion about three perpendicular axis allowing the connected body to rotate freely in any direction which is called as spherical joints so examples of revolute joints a robo arm with multiple revolute joints enables the arm to move in various things then Prismatic joint you you can carry it on a 3D printer where the precise linear movement is there cylindrical joints which can be used in telescopic mechanisms like shock abser and other things then you can have spherical joints which are used in your joystick or in your arm there can be a ball and then you can try to rotate it reol joints are widely used in machineries robotic arms Prismatic are used in CNC machines sliding doors cylindrical joint are used in Pistons telescopic mechanisms like shock absorb spherical joints are used in multi-direction movement in a vehicle suspension system or in robotic joints so now under mechanisms role of mechanisms in uh mechanical systems mechanisms are the building blocks of complex mechanical system systems they play a crucial role as discussed by guiding and controlling motion mechanisms enable machines to perform a wide variety of tasks so in different engineering applications machines Robo automobile systems these mechanisms are exhaustively used so some of the classifications of mechanism linear motion rotary motion oscillatory motion reciprocatory motion you can see here linear motion uh is a lock which is used a sliding drawer an elevator rotary motion it is rotation motion about a fixed axis something like a fan or a vehicle wheel oscillatory motion which is back and forth you can see this whatever it is it moves back and forth uh around the equilibrium position a pendulum or a swing reciprocating motion repeated linear motion back and forth which is used in engine pistons so inter relations and applications understanding the motion types is crucial for Designing mechanisms that convert one form of motion to the other so slider crank mechanism or crank slider mechanism it converts rotary motion of a crank into a reciprocatory motion in a piston Cam and follow mechanism trans rotary of your cam into oscillatory or linear motion so opening and closing of of some valves can be done by connecting it to a rotary motion quick return mechanism is a type of mechanical system designed to provide different speeds in the forward stroke and return stroke this is exhaustively used in machines and in particular it is used in shaping machine shaping machines so what it does is in the forward stroke it goes at a slower speed in the reverse stroke it goes at a faster speed so that's why it is called as quick return mechanism because in the return speed it's a non-productive so it has to be done very fast this type of mechanical systems designed to provide different speeds for the forward and the return the forward stroke typically moves slower and also precise while the return moves faster where it reduces the ideal time it is called as with worth quick return mechanism uh where in which this is a bull gear which is attached to a motor so this gear rotates and then you have a connecting rod so this connecting rod uh is connected to the bull gear like this and then you have a slotted bar in this the the connecting rod or this point keeps reciprocating up and down so this rotates this in turn transfers the motion to the stroke length whatever it is the mechanism converts rotary motion this is the rotary motion into a sliding motion or reciprocating motion in the forward Direction it is slow return Direction it is faster so application shaping machine this is how it is you see a a bull gear rotating and you have a uh slotted bar this slotted bar is connected to a link so this is how the in the forward stroke Machining happens return stroke it is non-productive so you get to move faster Cam and fall over you can see a slider which is there when the cam comes to the topmost position it pushes the reciprocating fall over and this fallover in turn slides inside and then opens and close a cam is an essential component in mechanical systems designed to convert rotary motion into oscillatory motion the shape or the profile of a cam directly influences the motion of a fall all over allowing a precise control of a complex mechanisms camps are particularly valuable because they can create nonuniform patterns such as accelerating or decelerating motion this exhaustive used in automobiles disc or plate cam it is a flat disc with a specific profile commonly used in engines cylindrical piston cams the it has a cylinder where the profile Cuts along the length used in Machine Tools translating motion it is a cam that moves in a straight line uh rather than rotating so these are all the different types of Cam you can have a a disk type cylinder type translation type follow there can be a flat-faced follow there can be a roller follow or there can be a knife edged follow so it has a flat surface in contact it basically to try to distribute the load it has a rolling element to reduce the friction which is your roller and you can have a knife which has a very precise control but it is prone for wear so valve timing in internal combustion engine is always done by Cam and follow in automation cams are used in automated machines which can be used in packaging textile and in assembly lines to recap what we have seen in this lecture we saw what is a linkage what are the different types of planer and spatial link linkage what is a four bar linkage then degrees of freedom calculation what is mechanisms and kinematic chain what is a function of a quick return mechanism I am sure you would have enjoyed this lecture uh and henceforth when you look at any machine or your door you should always look for what is the linkage and what is the mechanism the references used for this lecture are listed here thank you thank you very much [Music] [Music] [Music]