# What is Linkage: Definition and 99 Discussions

A mechanical linkage is an assembly of bodies connected to manage forces and movement. The movement of a body, or link, is studied using geometry so the link is considered to be rigid. The connections between links are modeled as providing ideal movement, pure rotation or sliding for example, and are called joints. A linkage modeled as a network of rigid links and ideal joints is called a kinematic chain.
Linkages may be constructed from open chains, closed chains, or a combination of open and closed chains. Each link in a chain is connected by a joint to one or more other links. Thus, a kinematic chain can be modeled as a graph in which the links are paths and the joints are vertices, which is called a linkage graph.

The movement of an ideal joint is generally associated with a subgroup of the group of Euclidean displacements. The number of parameters in the subgroup is called the degrees of freedom (DOF) of the joint.
Mechanical linkages are usually designed to transform a given input force and movement into a desired output force and movement. The ratio of the output force to the input force is known as the mechanical advantage of the linkage, while the ratio of the input speed to the output speed is known as the speed ratio. The speed ratio and mechanical advantage are defined so they yield the same number in an ideal linkage.
A kinematic chain, in which one link is fixed or stationary, is called a mechanism, and a linkage designed to be stationary is called a structure.

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1. ### Torque required to move robot arm (special linkage)

I need to calculate a torque required for uArm type of robot arm. Servos are at the base and 2 arms are controlled by system of linkage. I suppose all necessary info will be given by CAD, like weight and mass of gravity,etc.. But How would I properly size the servos? Is it the same as in classic...
2. ### I Link movement in X-Y-Z axis

i have this linkage as far as happening that This Link make angle between x-y axis and rotate also between x-y axis , meanwhilel yaw( z-axis) am i right ? please make it clear
3. ### Why the 4-pin linkage in heavy bolt cutters?

Why are these cutters made like this : ... rather than the simpler one-pin concept used in pliers and scissors?
4. ### I Determine ## \beta ## as a function of ##\theta## linkage

I 've been trying find ##\beta## as a function of ##\theta## for this linkage. It's quite the trigonometric mess. Start with the Law of Sines: $$\frac{\sin \beta}{x} = \frac{\sin \varphi}{R} \implies \boxed{ x = R \frac{\sin \beta}{\sin \varphi} \tag{1} }$$ Relating angles:  \theta +...
5. ### Simple Linkage with Reciprocating points

TL;DR Summary: Anybody help me get my head around this please Hi, If anybody could give me a steer on solving this that would be great. I am trying to solve the maximum forces at points fA and fB If the force from the drive TA = 64/0.6 = 1066.666N Point TB has equal arms so the same force...
6. ### Need help determine force from cylinder linkage

How can I determine the downward force of the rod with the given cylinder pressure and mechanical linkage? Do I sum my moments about the pivot? I calculated M=950xCOS(75.732)x7.81 + (X)SIN(63.414)x9.4 which resulted in 1828lbs. I get 217 lbs which does not seem right.
7. ### Four-Bar Parallel Linkage Pendulum

Hello, I'm new here and I'm looking for advice regarding some calculations of a device I constructed/should construct. It's a 4 bar (parallel) linkage system, which is used like a pendulum. It is released from a certain height, with just the gravity acting on it. I understand how to calculate...
8. ### Find the angular velocity of this linkage

Hi! everyone! ;) I have a problem with the development of this problem. I need to resolve it with 2 procedures: trigonometry and instant centers. My advance can be see in the next image: The instant centers procediment its (1) up and trigonometry procediment its (2) down. I know that the...
9. ### Instantaneous centers of a six bar linkage

I am not sure how to relate the velocities of P 2,6 and slider D. The textbook solution states that they are equal but can someone explain how this can be proven? As far as I understand if P 2,6 is considered as a point on the extended link 2 then it has the same linear velocity as link 6 but...
10. ### Equivalence of various forms of flux linkage

Hello all, Apologies if this has already been asked before, but I tried researching this question for a while with no results. I was reading Grainger's Power System Analysis' derivation of the inductance of a single wire and got confused by his definition of magnetic flux linkage. He seems to...
11. ### Calculation of Change in Magnetic Flux Linkage of a moving wire

Can anyone explain the above answer to me? What does the "change in area" mean?
12. ### Linkage Analysis and force study

Hi All, I am working on this linkage mechanism. Please see the attachment for images. There are 3 pivot points. Two of which are connected to the ground. The" Inside Leg 1" is telescopic to "Leg 2" and has a 120 LB compression gas spring connected at mount points as shown in the image. The leg...
13. ### Proper barograph linkage settings for maximum pen displacement?

Hi. I wasn't sure where to post this. It does relate to Earth science, but still wasn't sure whether or not to post there. Anyway, I am trying to determine the proper settings of the linkage of my barograph so that the pen moves the greatest distance up or down on the chart with as minimal...
14. ### Linkage design for Excavator and Dump truck

Hi, I need to know the name of some very good books for learning linkage design. I have to design some complex system using Linkage. I have to design excavator, truck and crane and hydraulics machines and civil Engineering Machnies, Agriculture machines, robot arm. I have a little knowledge in...
15. ### 4 Linkage system: velocity calculation

For the attempt at a solution view the Excel screenshots (1). A screenshot with all the lengths is provided (2). The 4-linkage system is shown in screenshot (3). The problem is shown in screenshot (4). A screenshot from the whole assembly is also provided to add some insights (5). Thanks...
16. ### Linkage analysis of forces and stresses?

The attached image shows a linkage mechanism with 2 parallel bars pivoted to a fixed base. The lengths of the the bars are equal. A connecting linkage and gears are used to connect it to a 3rd bar. I would like to know how to analyze this linkage system to find the forces, moments and loads for...
17. ### Getting very low flux linkage in ANSYS Maxwell

I'm new to ANSYS Maxwell and I'm trying to follow the inductance calculation example in the user's guide. The results for the inductance are pretty close but the value of flux are very low. What cause this? What should I do?
18. ### How to determine the force on the linkage

hi Wondering if someone could help. I need to know how to work out the the force at point 'A' ( see sketch attached). Its a door opening and closing mechanism and it consists of a hydraulic cylinder 32mm dia bore operating at 140 bar. The door is opened and closed via couple of linkages as the...
19. ### Inducing currents without change of flux linkage?

Suppose I had cylindrically-symmetric rotating magnet surrounded by a plasma. I rotate it on its axis at a constant angular velocity, and so the electric field E produced is non-solenoidal and can be described as the negative gradient of some potential V(x,y,z). The electric field is induced...
20. ### RTG crane -- hydraulic motor and linkage design to turn these wheels

Hi all I would like to ask your professional guide in designing a hydraulic system. I attached a file, showing sketch of the RTG crane wheel structure. Here are the conditions: 1. The red-line is the hydraulic cylinder with "X" as the fix point. 2. The hydraulic cylinder will stroke out from...
21. ### Calculation of Change in Magnetic Flux Linkage Across a Wire

Homework Statement A straight wire of length 0.20m moves at a steady speed of 3.0m/s at right angles to a magnetic filed of flux density 0.10T. Use Faraday's law to determine the e.m.f. induced across the ends of a wire. Homework Equations E= Nd Φ/dt but N=1 so E= dΦ/dt The Attempt at a...
22. ### Four Bar Linkage Mechanism - Space Diargram

Homework Statement A four bar chain is arranged as the diagram shown below If the input link AB rotates at 400 RPM anti CW determine the angular velocity of link DC Homework Equations See attached photo The Attempt at a Solution See attached photo
23. P

### Behavior of inductors -- Why flux linkage does not change instantaneously?

Why is it that the flux linkage does not change instantaneously ? is it some property of magnetic fields?
24. ### The rate of change in the magnetic field linkage in a coil

Hi, I would appreciate it if someone explains the difference between these two phases regarding a coil rotates in a uniform magnetic field. 1. The rate with which the coil intercepts the lines of magnetic field in the dynamo is maximum when the plane of the coil is parallel to the lines of the...
25. ### Torque around a point from lever linkage

Hi all. Brushing up on some of my force and torque stuff so I can do some modelling in software. Homework Statement I have a system as shown in the picture. A force F acts at point A, which is the end point of the lever AB. Connected to the lever is a link BC, and connected to BC at point C is...
26. ### MCQ - Independent assortment or Incomplete linkage

Homework Statement Two flies were crossed one wildtype another double mutant sepia(se) and vestigial(vg) yielding 40% wild type 40% se vg, 10% se and 10% vg. The genes show- a.Complete linkage b.Incomplete linkage c.Independent assortment d. epistasis 2. The attempt at a solution Since no. of...
27. ### What is linkage strength between gene loci?

Homework Statement In linkage strength between any two gene loci is 70%,what would be the amount of crossing over between these loci? (a) 15% (b)30% (c) 70% (d) none of these. 2. My approach at understanding the concept I didn't find much about linkage strength from any authentic source. I...
28. ### Velocity of linkage arm end

Homework Statement I uploaded the picture to this problem, but it asks what the relative velocity of point p is to point o when theta is equal to one and the derivative of theta in respect to time is also positive 1. the picture explains everything. Homework Equations Tangential velocity...
29. ### Static Force Analysis of Linkage

Hi! I'm trying to complete a static force analysis on the bar linkage shown below. The goal is to find the payload mass in terms of the cylinder forces and everything else in a static environment. To simplify things I've made the assumption that the mass of the payload in the bucket acts at...
30. ### Free Body Diagram of 3-Bar Linkage. Splitting the force?

Homework Statement Hi, please see the attached file. I am trying to find the force as illustrated in the diagram. Homework Equations [/B] The Attempt at a Solution I've found the force for the 4deg beam and therefore the horizontal beam however I am unsure how to take into account the...
31. ### Understanding the four bar linkage DOF

Hello guys, I have a doubt with understanding DOFs. I have taken the example of the four bar linkage. According to Grueblr's condition, the DOF of this mechanism is 1. \mbox{DOF} = 3(l-1) + 2j_1 + 2j_2\\l=4\ j_1=4\ j_2=0\\\mbox{DOF} = 1 In the above figure, the links next to the ground link...
32. ### Kinematics of a four bar linkage system

Homework Statement Homework Equations N/A The Attempt at a Solution I have 2 (basic) questions about this system: 1) The question says that ωAB = ωABk, I understand that bold indicates vectors whilst the plain text indicates a magnitude so ωAB (magnitude) multiplied by k (direction vector)...
33. ### Automotive Single actuator Wiper design to wipe a surface area

I'm given this problem to solve with the assumption as stated above. The answers need not be logical as long as the linkage mechanism can be simulated. I've attempted the question using Mercedes Mono Wiper mechanism but only manage to cover 41% given the width of the wiper. May I ask if there...
34. ### Four bar linkage odd behaviour? (Simscape Multibody)

Dear community, I posted this thread in Mathworks Simscape Community two days ago or so. And I have decided to record a video and post all the information in this forum. This is my first time, so hello and thanks for reading! Last month I was playing around with Simscape Multibody and I...
35. ### Understanding solution method for finding accelerations in a mechanical linkage

Homework Statement I was checking my work and Chegg uses the equations differently. Can somebody tell me why? Maybe I'm misunderstanding how/why to use the equation I chose. Homework Equations They say aB = -ω2ABRB/Ai I used aB = aA + αk x r - ω2rB/A The Attempt at a Solution So obviously...
36. ### How is emf constant of flux linkage is increasing?

how is this true? I get that it's the rate of change of flux, and if you have a graph of flux linkage against time, the gradient with a constant gradient then emf is constant since it IS the gradient... But how? If the flux linkage is increasing, why doesn't the emf?
37. ### Help with movable joint parts

I want to make a simple slider crank mechanism. I don't know what type of bolts or whatever is used for movable arms. I've heard online so far that using a carage bolt and nylon lock nut will work, but I bet there's probably other ways to make a movable joint. Something more secure. I'm sure...
38. ### How to specify parameters via calculations in 4 bar linkage

Hi I'm looking to design a 4 bar compound linkage. I know how torque, force, power and angular velocity are transferred on four bar mechanisms. Could someone help me with compound four bar calculations? http://i66.tinypic.com/2jg6z9t.jpg The lower arrow shoes the input torque. I need to design...
39. ### Velocity diagram for 4 bar linkage

Homework Statement http://photouploads.com/images/017db8.png http://photouploads.com/images/eebec7.png http://photouploads.com/images/f472e6.png Homework Equations v= rω The Attempt at a Solution I don't really have much of an attempt. I missed this lecture so I am completely confused on how...

Homework Statement Homework Equations M = 3(L – 1) – 2J L= number of links, J = number of joints The Attempt at a Solution As far as I can see, using the above L and J values for each linkage yields the correct M value. However, the L and J values lead me to think I'm missing something...
41. ### Magnetic Flux Linkage: Rate of Change & Cutting

Hi, this may be really easy but.. I understand that to have an induced e.m.f , we can either have a rate of change of magnetic flux linkage ( ac source ) or cutting of flux ( like a plate oscillating and cutting through a magnetic field produced by a solenoid ). However does cutting of flux...
42. ### Flux linkage in a wire coil

Flux linkage in a wire coil is given by BANcos(theta) with B being flux density, N being the number of turns in a coil and A being the cross sectional area of the coil and theta being the angle between the normal to the plane of the coil and the magnetic field. Is anybody able to explain why it...
43. ### Flux linkage in inductance calculation for single wire.

Hello. Maybe this is the one of the most typical example in Electromagnetism textbook. There is a single round wire carrying current I (in D.C) with radius of R and length is infinity. From Ampere's law, the B field inside the wire is B = μIρ/2πR2 aθ where ρ is radial distance from...
44. ### Synthesis of a four bar linkage with a ternary couplar

Hi there! Currently i am trying to design a four bar linkage for a bicycle rear shock. You can find this linkage at here http://ffden-2.phys.uaf.edu/211_fall2010.web.dir/Michael_Stanfill/VirtualPivot.html This linkage is called virtual pivot point. Critical part of this design is to achieve a...
45. ### Clarifying the notion of Flux Linkage

Hello! Im having some trouble really understanding this concept. I'll summarize my difficulty in 2 situations that I struggle with: 1) Coil: The inductance of a coil with N turns is known to be proportional to N2. My question is why is that true? I know that the H-field (and therefore the...
46. ### Help me understand magnetic flux linkage

Magnetic flux linkage = BAN B=magnetic field strength per unit area A=Area of conductor moved through the magnetic field N=Number of coils I don't understand when my physics textbook says the area of a single coil of wire moved through the magnetic field is π×radius of coil^2 as most of the...
47. ### Induction and flux linkage clarification

So if you have a single inductor then I assume that there is no flux linkage and that L = flux*N / i = L11 and so that flux is total leakage flux. If you have two inductors then the flux leakage is any flux that isn't flux linkage (the self flux is flux leakage). (flux21 is the flux in 2 from...
48. ### Finding Offspring Phenotypes from AB/ab Mating: Linkage Questions

Genes A/a and B/b are linked and known to be 20 map units apart. Individuals heterozygous for both of these genes (genotypes= AB/ab) were mated with each other. If there 2000 offspring from this cross, how many of the offspring would you expect to show Ab or aB phenotypes? I know that the...
49. ### Magnetic flux linkage and area as a vector

Homework Statement A circular coil of diameter 24 mm has 40 turns. The coil is placed in a uniform magnetic field of flux density 85 mT with its plane perpendicular to the field lines. a) i Calculate the area of the coil ii The flux linkage through the coil. b) The coil was reversed in a...
50. ### Constraints for Linkage system

Hi guys! I have a question on applying constraint on Linkage systems. Assumed that there is a two dimensional one-bar linkage, one end can only rotate and one end is free (Such as the figure above, please neglect the damper-spring system if you want). This link can rotate only 180 degrees, not...