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Locking pliers exemplify a four-bar, one degree of freedom mechanical linkage; or a five-bar, two DOF linkage when the adjustment screw is considered.
Locking pliers exemplify a four-bar, one degree of freedom mechanical linkage; or a five-bar, two DOF linkage when the adjustment screw is considered. Pliers are Hand tools designed primarily for gripping objects by using Leverage. In mechanics, degrees of freedom (DOF are the set of independent displacements and/or rotations that specify completely the displaced or deformed position and orientation

A mechanical linkage is a series of rigid links connected with joints to form a closed chain, or a series of closed chains. Each link has two or more joints, and the joints have various degrees of freedom to allow motion between the links. In mechanics, degrees of freedom (DOF are the set of independent displacements and/or rotations that specify completely the displaced or deformed position and orientation A linkage is called a mechanism if two or more links are movable with respect to a fixed link. A machine is any device that uses Energy to perform some activity Mechanical linkages are usually designed to take an input and produce a different output, altering the motion, velocity, acceleration, and applying mechanical advantage. In Physics and Engineering, mechanical advantage (MA is the factor by which a mechanism multiplies the force put into it

A linkage designed to be stationary is called a structure.

Contents

History

A flyball governor for flow control. A water turbine spins the governor, which controls the water flow, which feeds the turbine, creating a speed-regulated machine.
A flyball governor for flow control. A centrifugal governor is a specific type of governor that controls the Speed of an Engine by regulating the amount of Fuel (or Working A water turbine spins the governor, which controls the water flow, which feeds the turbine, creating a speed-regulated machine. A water turbine is a rotary Engine that takes energy from moving water

Mechanical linkages are a fundamental part of machine design, and yet many simple linkages were not well understood nor invented until the 19th century. Consider a stick: it has six degrees of freedom, three of which are the coordinates of its centre in space, the other three describing its rotation. Once nudged between a boulder and fulcrum it is constrained to a particular motion, to act as a lever to move the boulder. In Geology, a boulder is a rock with grain size of usually no less than 256 mm (10 Inches diameter When more links are added and joined in various ways their collective motion can be further defined. Very complicated and precise motions can be designed into a linkage with only a few parts.

The Industrial Revolution was the golden age of mechanical linkages. The Industrial Revolution was a period in the late 18th and early 19th centuries when major changes in agriculture manufacturing and transportation had a profound effect on the Mathematical, engineering and manufacturing advances provided both the need and the ability to create new mechanisms. Many simple mechanisms that seem obvious today required some of the greatest minds of the era to create. Leonhard Euler was one of the first mathematicians to study linkage synthesis, and James Watt worked very hard to invent the Watt linkage to support his steam engine's piston. James Watt ( 19 January 1736 &ndash 25 August 1819 Boulton proved to be an excellent businessman and both men eventually made fortunes This article concerns parallel motion in mechanics For parallel motion in music see the article Contrary motion. A steam engine is a Heat engine that performs Mechanical work using Steam as its Working fluid. Chebyshev worked on mechanical linkage design for over thirty years, which led to his work on polynomials2. Pafnuty Lvovich Chebyshev (Пафну́тий Льво́вич Чебышёв ( –) was a Russian Mathematician. In Mathematics the Chebyshev polynomials, named after Pafnuty Chebyshev, are a sequence of Orthogonal polynomials which are related to A mechanical linkage is a series of rigid links connected with joints to form a closed chain or a series of closed chains New linkage inventions, designed by need, were instrumental in cloth making, power conversion and speed regulation. The first power loom, a mechanized Loom powered by a Drive shaft, was designed in 1784 by Edmund Cartwright and first built in 1785 later to be perfected Even the ability of a mechanism to produce accurate linear motion, without a reference guide way, took years to solve.

Scientists, mostly German, Russian and English, have researched this domain over the last 200 years, so that today most traditional analysis or synthesis problems (e. g. planar movement) have been solved (see online libraries under External links). Recently, compliant structures have come to the fore.

Electronic technology has replaced many linkage applications taken for granted today, such as mechanical computation, typewriting and machining. However, modern linkage design continues to advance, and designs that used to occupy an engineer for days are now optimized with a computer in seconds.

Even though servomechanisms with digital control are common, and at first glance easy to use, some motion problems (especially for quick and accurate movements) are still only soluble using linkages and cams. A servomechanism, or servo is an automatic device which uses error-sensing Feedback to correct the performance of a mechanism

Theory

The most common linkages have one degree of freedom, meaning that there is one input motion that produces one output motion. Most linkages are also planar, meaning all the motion takes place in one plane. Spatial linkages (non-planar) are more difficult to design and therefore not as common.

Kutzbach-Gruebler's equation is used to calculate the degrees of freedom of linkages. The number of degrees of freedom of a linkage is also called its mobility.

A simplified version of the Kutzbach-Gruebler's equation for planar linkages :

m = 3(n-1)-2j \,
m \, = mobility = degrees of freedom
n \, = number of links (including a single ground link)
j \, = number of one-degree-of-freedom kinematic pairs (pin or slider joints)
Linkage mobility


A more general form of the Kutzbach-Gruebler equation for planar linkages involving more complex joints:

m = 3(n-j-1)+ \sum_{n=1}^j\ f_i,

Or, for spatial linkages (linkages involving 3D motion):

m = 6(n-j-1)+ \sum_{n=1}^j\ f_i,
m \, = mobility (degrees of freedom)
n \, = number of links (including a single ground link)
j \, = number of total joints, regardless of connectivity or degree-of-freedom
\sum_{n=1}^j\ f_i= sum of each joint's individual degree of freedom

The mobility of hydraulic machinery can easily be identified by counting the number of independently controlled hydraulic cylinders. Hydraulic machinery are machines and tools which use Fluid power to do work

Simple linkages are capable of producing complicated motion.
Simple linkages are capable of producing complicated motion.

Types of common joints:

Designers will synthesize a linkage by starting with the required output motion, mechanical advantage, velocity and acceleration. A type of linkage is chosen and modified to deliver the required performance.

Each link is treated as a vector and the vectors can be combined into a system of equations because they form a loop. The matrix is solved to create a closed form equation that relates input motion to output motion. The same is done for mechanical advantage, or any other important quantity. In Physics and Engineering, mechanical advantage (MA is the factor by which a mechanism multiplies the force put into it The equations of motion are differentiated with respect to time to find velocity and acceleration of the mechanism parts. In Calculus, a branch of mathematics the derivative is a measurement of how a function changes when the values of its inputs change

Types of linkages

Four bar linkages are the simplest closed loop kinematic linkage. A four bar linkage or simply a 4-bar or four-bar is the simplest movable linkage. They perform a wide variety of motions with a few simple parts. They were also popular in the past due to the ease of calculations, prior to computers, compared to more complicated mechanisms.

Types of four bar linkages, s = shortest link, l = longest link
Types of four bar linkages, s = shortest link, l = longest link


Other notable types of linkages;

A function generator linkage that approximates a parabolic output.
A function generator linkage that approximates a parabolic output. In Mathematics, the parabola (pəˈræbələ from the Greek παραβολή) is a Conic section, the intersection of a right circular

Uses

A spatial 3DOF linkage for joystick applications.
A spatial 3DOF linkage for joystick applications. The Chebyshev linkage is a mechanical linkage that converts rotational motion to approximate straight-line motion The Hoekens linkage is a Four bar mechanism that converts rotational motion to approximate straight-line motion The Sarrus linkage, invented in 1853 by Pierre Frédéric Sarrus, is a mechanical linkage to convert a limited circular motion to a linear motion without reference

Linkages are primarily used as machine components and tools. A machine is any device that uses Energy to perform some activity A broader definition of a tool is an entity used to interface between two or more domains that facilitates more effective action of one domain upon the other Typical examples are automotive suspensions and bolt cutters. Suspension is the term given to the system of springs, Shock absorbers and linkages that connects a Vehicle to its Wheels Suspension A bolt cutter, sometimes called bolt cropper, is a tool used for cutting chains padlocks Bolts and wire mesh The internal combustion engine's piston/rod/crank is a classic four-bar linkage with one degree of freedom. Linkages are often the simplest, least expensive and most efficient mechanism to perform complicated motions.

One highly visible application is the windshield wiper: a four bar linkage changes the motor's rotary motion to oscillation. A windscreen wiper ( windshield wiper in North America) is a device used to wipe Rain and dirt from a Windscreen. Some wipers also have a second set of four bar linkages to keep the wiper blades oriented correctly as they sweep. Another visible application is heavy equipment which makes extensive use of four and six bar linkages. Engineering vehicles, known by the other terms construction Equipment, earth movers heavy equipment or just plain equipment are machines specifically designed to execute

Spatial linkages are becoming more common due to computer aided design.

"The 4-Bar Linkage" is an adapted mechanical linkage used on bicycles. With a normal full-suspension bike the back wheel moves in a very tight arc shape. This means that more power is lost when going uphill. With a bike fitted with a 4-Bar Linkage, the wheel moves in such a large arc that it is moving almost vertically. This way the power loss is reduced by up to 30%.

References

  1. Erdman, Arthur G. ; Sandor, George N. (1984). Mechanism Design: Analysis and Synthesis. Prentice-Hall. ISBN 0-13-572396-5.  
  2. How to Draw a Straight Line, historical discussion of linkage design
  3. What is a Watt I Linkage?

See also

External links

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