A straight-line mechanism is a
mechanism
Mechanism may refer to:
*Mechanism (engineering), rigid bodies connected by joints in order to accomplish a desired force and/or motion transmission
*Mechanism (biology), explaining how a feature is created
*Mechanism (philosophy), a theory that a ...
that converts any type of rotary or angular motion to perfect or near-perfect straight-line motion, or ''vice-versa''. Straight-line motion is
linear motion
Linear motion, also called rectilinear motion, is one-dimensional motion along a straight line, and can therefore be described mathematically using only one spatial dimension. The linear motion can be of two types: uniform linear motion, with co ...
of definite length or "stroke", every forward stroke being followed by a return stroke, giving
reciprocating motion
Reciprocating motion, also called reciprocation, is a repetitive up-and-down or back-and-forth linear motion. It is found in a wide range of mechanisms, including reciprocating engines and pumps. The two opposite motions that comprise a single r ...
.
The first such mechanism, patented in 1784 by
James Watt
James Watt (; 30 January 1736 (19 January 1736 OS) – 25 August 1819) was a Scottish inventor, mechanical engineer, and chemist who improved on Thomas Newcomen's 1712 Newcomen steam engine with his Watt steam engine in 1776, which was fun ...
, produced approximate straight-line motion, referred to by Watt as
parallel motion
In kinematics, the parallel motion linkage is a six-bar mechanical linkage invented by the Scottish engineer James Watt in 1784 for the double-acting Watt steam engine. It allows a rod moving practically straight up and down to transmit moti ...
.
Straight-line mechanisms are used in a variety of applications, such as engines, vehicle suspensions, walking robots, and rover wheels.
History
In the late eighteenth century, before the development of the
planer The term planer may refer to several types of carpentry tools, woodworking machines or metalworking machine tools.
*Plane (tool), a hand tool used to produce flat surfaces by shaving the surface of the wood
*Thickness planer (North America) or thi ...
and the
milling machine
Milling is the process of machining using rotary cutters to remove material by advancing a cutter into a workpiece. This may be done by varying direction on one or several axes, cutter head speed, and pressure. Milling covers a wide variety of d ...
, it was extremely difficult to machine straight, flat surfaces. During that era, much thought was given to the problem of attaining a
straight-line motion
Linear motion, also called rectilinear motion, is one-dimensional motion along a straight line, and can therefore be described mathematically using only one spatial dimension. The linear motion can be of two types: uniform linear motion, with co ...
, as this would allow the flat surfaces to be machined. To find a solution to the problem, the first straight line mechanism was developed by
James Watt
James Watt (; 30 January 1736 (19 January 1736 OS) – 25 August 1819) was a Scottish inventor, mechanical engineer, and chemist who improved on Thomas Newcomen's 1712 Newcomen steam engine with his Watt steam engine in 1776, which was fun ...
, for guiding the piston of early steam engines. Although it does not generate an exact straight line, a good approximation is achieved over a considerable distance of travel.
Perfect straight line linkages were later discovered in the nineteenth century, but they weren't as needed, as by then other techniques for machining had been developed.
List of linkages
Approximate straight line linkages
These mechanisms often utilize
four bar linkages as they require very few pieces. These four-bar linkages have
coupler curves that have one or more regions of approximately perfect straight line motion. The exception in this list is Watt's parallel motion, which combines Watt's linkage with another four-bar linkage – the
pantograph
A pantograph (, from their original use for copying writing) is a mechanical linkage connected in a manner based on parallelograms so that the movement of one pen, in tracing an image, produces identical movements in a second pen. If a line dr ...
– to amplify the existing approximate straight line movement.
It is not possible to create perfectly straight line motion using a four-bar linkage, without using a
prismatic joint
A prismatic joint is a one- degree-of-freedom kinematic pair which constrains the motion of two bodies to sliding along a common axis, without rotation; for this reason it is often called a slider (as in the slider-crank linkage) or a sliding p ...
.
*
Watt's linkage
In kinematics, Watt's linkage (also known as the parallel linkage) is a type of mechanical linkage invented by James Watt in which the central moving point of the linkage is constrained to travel on a nearly straight line. It was described in W ...
(1784)
*
Watt's parallel motion (1784)
*
Evans "Grasshopper" linkage
Evans may refer to:
People
*Evans (surname)
*List of people with surname Evans
Places United States
*Evans Island, an island of Alaska
*Evans, Colorado
*Evans, Georgia
*Evans County, Georgia
*Evans, New York
*Evans Mills, New York
*Evans City, ...
(1801)
*
Chebyshev linkage
In kinematics, Chebyshev's linkage is a four-bar linkage that converts rotational motion to approximate linear motion.
It was invented by the 19th-century mathematician Pafnuty Chebyshev, who studied theoretical problems in kinematic mechanism ...
*
Chebyshev lambda linkage
In kinematics, the Chebyshev Lambda Linkage is a four-bar linkage that converts rotational motion to approximate straight-line motion with approximate constant velocity. It is so-named because it looks like a lowercase Greek letter lambda (λ) ...
(1878) - a
cognate linkage
In kinematics, cognate linkages are linkages that ensure the same coupler curve geometry or input-output relationship, while being dimensionally dissimilar. In case of four-bar linkage coupler cognates, the Roberts–Chebyshev Theorem, after ...
of the Chebyshev linkage
*
Roberts linkage
A Roberts linkage is a four-bar linkage which converts a rotational motion to approximate straight line mechanism, straight-line motion.
The linkage was developed by Richard Roberts (engineer), Richard Roberts.
The Roberts linkage can be classif ...
*
Horse-head linkage
*
Hoecken linkage
In kinematics, the Hoecken linkage (named for Karl Hoecken) is a four-bar linkage that converts rotational motion to approximate straight-line motion. The Hoecken linkage is a cognate linkage of the Chebyshev linkage and Chebyshev's Lambda Mech ...
(1926) - requires a sliding joint
Perfect straight line linkages
Eventually, perfect straight line motion would be achieved.
The Sarrus linkage was the first perfect linear linkage, made in 1853. However, it is a spatial linkage rather than a planar linkage. The first planar linkage would not be made until 1864.
Currently, all planar linkages which produce perfect linear motion utilize the
inversion around a circle to produce a hypothetical circle of infinite radius, which is a line. This is why they are called inversors or inversor cells.
The simplest solutions are Hart's W-frame – which use 6-bars – and the Quadruplanar inversors – Sylvester-Kempe and Kumara-Kampling, which also use 6-bars.
*
Sarrus linkage
The Sarrus linkage, invented in 1853 by Pierre Frédéric Sarrus, is a mechanical linkage to convert a limited circular motion to a linear motion or vice versa without reference guideways. It is a spatial six-bar linkage (6R) with two groups ...
(1853)
*
Peaucellier-Lipkin inversor (1864)
*
Hart's first inversor / Hart's antiparallelogram / Hart's W-frame (1874)
*
Hart's second inversor / Hart's A-frame (1875)
*
Perrolatz inversor
*
Kempe's double kite inversors (1875)
*
Bricard inversor
*
Quadruplanar inversor
The Quadruplanar inversor of Sylvester and Kempe is a generalization of Hart's inversor. Like Hart's inversor, is a mechanism that provides a perfect straight line motion without sliding guides.
The mechanism was described in 1875 by James Josep ...
(1875)
The
Scott Russell linkage
A Scott Russell linkage is a linkage which translates linear motion through a right angle.
The linkage is named after John Scott Russell (1808–1882), although watchmaker William Freemantle had already patented it in 1803.
A different form of ...
(1803) translates linear motion through a right angle, but is not a straight line mechanism in itself. The
Grasshopper beam/Evans linkage, an approximate straight line linkage, and the Bricard linkage, an exact straight line linkage, share similarities with the Scott Russell linkage and the
Trammel of Archimedes
A trammel of Archimedes is a mechanism that generates the shape of an ellipse. () It consists of two shuttles which are confined ("trammeled") to perpendicular channels or rails and a rod which is attached to the shuttles by pivots at fixed posi ...
.
Compound eccentric mechanisms with elliptical motion
These mechanisms use the principle of a
rolling curve instead of a
coupler curve and can convert continuous, rather than just limited, rotary motion to reciprocating motion and ''vice versa'' via elliptical motion. The straight-line sinusoidal motion produces no second-order inertial forces, which simplifies
balancing in high-speed machines.
*
Cardan straight line mechanism. Using the principle of the
Tusi couple
The Tusi couple is a mathematical device in which a small circle rotates inside a larger circle twice the diameter of the smaller circle. Rotations of the circles cause a point on the circumference of the smaller circle to oscillate back and fort ...
(1247), a
spur gear
Spur gears or straight-cut gears are the simplest type of gear. They consist of a cylinder or disk with teeth projecting radially. Viewing the gear at 90 degrees from the shaft length (side on) the tooth faces are straight and aligned parallel to ...
rolls inside an internally toothed
ring gear
An epicyclic gear train (also known as a planetary gearset) consists of two gears mounted so that the center of one gear revolves around the center of the other. A carrier connects the centers of the two gears and rotates the planet and sun gea ...
of twice the diameter. The
hypocycloid
In geometry, a hypocycloid is a special plane curve generated by the trace of a fixed point on a small circle that rolls within a larger circle. As the radius of the larger circle is increased, the hypocycloid becomes more like the cycloid crea ...
traced by any point on the pitch circle of the smaller gear is a diameter of the larger gear. The mechanism has been used in
Murray's Hypocyclic Engine.
*
Trammel of Archimedes
A trammel of Archimedes is a mechanism that generates the shape of an ellipse. () It consists of two shuttles which are confined ("trammeled") to perpendicular channels or rails and a rod which is attached to the shuttles by pivots at fixed posi ...
. Originally an ellipsograph. As a mechanism, it uses the fact that a circle and a straight line are special cases of an ellipse. It is based on much the same kinematic principle as Cardan's straight line mechanism (above) and could be considered as a spur gear with two teeth in a ring gear with four teeth. It has been used in the Baker-Cross engine. It has been used in inverted form in Parsons' steam engine and can still be found today in a further inversion as the
Oldham coupling
A coupling is a device used to connect two shafts together at their ends for the purpose of transmitting power. The primary purpose of couplings is to join two pieces of rotating equipment while permitting some degree of misalignment or end mov ...
.
*MultiFAZE mechanism. The Multiple Fixed Axis Shaft Compound Eccentric mechanism also uses elliptical motion, but here the contrarotating parts are not coaxial, but separated laterally, and the drive between them is transmitted by spur gears instead of a bearing, to reduce friction and wear. The mechanism has been used in a cantilever configuration in the Stiller-Smith engine.
Clean engines - A combination of advanced materials and a new engine design
/ref>
Gallery
Approximate straight line linkages
Parts/links of the same color are the same dimensions.
File:Watts Linkage.gif, Watt's linkage
File:Watts Parallel Motion Linkage.gif, Watts parallel motion linkage
File:Evans "Grasshopper" Linkage.gif, Evans "Grasshopper" linkage
File:Roberts Linkage.gif, Roberts linkage
File:Chebyshev Linkage.gif, Chebyshev linkage
File:Chebyshev Lambda Linkage.gif, Chebyshev lambda linkage
File:Chebyshev Table Linkage.gif, Chebyshev table linkage
File:Hoecken's Linkage.gif, Hoecken's linkage
Perfect straight line linkages
Parts/links of the same color are the same dimensions.
File:Sarrus Linkage - Links Ver.gif, Sarrus linkage (Bars variant)
File:Sarrus Linkage.gif, Sarrus linkage (Plates variant)
File:Peaucellier-Lipkin Inversor.gif, Peaucellier-Lipkin inversor
File:Harts Inversor 1.gif, Harts inversor 1
File:Harts Inversor 2.gif, Harts inversor 2 [
File:Perrolatz Inversor.gif, Perrolatz inversor
File:Kempe Kite Inversor 1.gif, Kempe kite inversor 1 ][
File:Kempe Kite Inversor 2.gif, Kempe kite inversor 2 ][
File:Kempe Kite Inversor 3.gif, Kempe kite inversor 3 ][
File:Scott Russell Linkage.gif, Scott Russell linkage (slider connection) ][
File:Scott Russell Demonstration.gif, Scott Russell linkage (connected to Peaucellier-Lipkin linkage)
File:Bricard Inversor.gif, Bricard inversor ][
File:Quadruplanar Inversor 1.gif, Sylvester-Kempe quadruplanar inversor 1 ][
File:Quadruplanar Inversor 2.gif, Sylvester-Kempe quadruplanar inversor 2 ][
File:Quadruplanar Inversor 3.gif, Sylvester-Kempe quadruplanar inversor 3
File:Quadruplanar Inversor 4.gif, Kumara-Kampling inversor ][
]
Tusi couple, elliptical motion: versions and inversions
File:T1 Tusi diag 90x20.gif, Tusi couple according to the diagrams in the translation of the copy of Tusi's original description: Small circle rolls within large circle.
File:T2 Tusi descr 90x20.gif, Tusi couple according to the translation of the copy of Tusi's original description: Circles rotate in same direction, speed ratio 2:1.
File:Tusi by Copernicus 90x20.gif, Copernicus' take on the Tusi couple: Direction of rotation and orbit of moving circle are equal and opposite.
File:T4 Inv4 90x20.gif, Inversion No. 3
File:T9 Inv4 90x20.gif, Inversion No. 4
File:Parsons 190x20.gif, Parsons' mechanism is a doubled-up version of Tusi couple Inversion No. 2 linked by an Archimedes trammel.
File:Oldham 120x30.gif, Oldham coupling. Slot- ted ends of two shafts (black) are coupled by cross piece (green). Compare with Tusi couple Inversion No. 4.
File:MultiFAZE 150x25.gif, Kinematics of the MultiFAZE mechanism characterised by parallelogram ABCD. The large broken circle is for reference only.
Compound eccentric mechanisms with elliptical motion
File:Tusicardmedes 120x40.gif, A spur gear with two teeth rolls inside a ring gear with four teeth: Archimedes, Tusi or Cardano?
File:Cardano's hypocyclic gears.gif, Cardan's hypocyclic gear pair: the red, green and blue pins move in straight lines.
File:Triple trammel of Archimedes.gif, Three Archimedes trammels on a triangular rotor showing the circular orbit of the trammel midpoints.
File:MultiFAZE_60°_X4 100x40.gif, 60° X4 engine with MultiFAZE mechanism with counterweights for full balance.
See also
*Four-bar linkage
In the study of mechanisms, a four-bar linkage, also called a four-bar, is the simplest closed- chain movable linkage. It consists of four bodies, called ''bars'' or ''links'', connected in a loop by four joints. Generally, the joints are configu ...
*Linkage (mechanical)
A mechanical linkage is an assembly of systems 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 i ...
*Rigid chain actuator
A rigid chain actuator, known variously as a linear chain actuator, push-pull chain actuator, electric chain actuator or column-forming chain actuator, is a specialized mechanical linear actuator used in window operating, push-pull material handl ...
Notes
References
* Theory of Machines and Mechanisms, Joseph Edward Shigley
External links
Cornell university (archived)
- Straight-line mechanism models
*
* {{cite web , url=http://pi.math.cornell.edu/~dwh/courses/M451-F02/PL-2.htm , title=How to Draw a Straight Line - a tutorial , author=Daina Taimina , author-link=Daina Taimina , website=Cornell University
Cornell University is a private statutory land-grant research university based in Ithaca, New York. It is a member of the Ivy League. Founded in 1865 by Ezra Cornell and Andrew Dickson White, Cornell was founded with the intention to teach an ...
Simulations
using the Molecular Workbench software
- Hart's A-frame (draggable animation) 6-bar linkage
Linkages (mechanical)
Linear motion
Straight line mechanisms