A straight-line mechanism is a
mechanism 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 of definite length or "stroke", every forward stroke being followed by a return stroke, giving
reciprocating motion.
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 ...
, produced approximate straight-line motion, referred to by Watt as
parallel motion.
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 and the
milling machine, 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 ...
, 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 – 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 ...
(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 mechan ...
*
Chebyshev lambda linkage (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
*
Horse-head linkage
*
Hoecken linkage (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 (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 (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 o ...
(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 pos ...
.
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 (1247), a
spur gear rolls inside an internally toothed
ring gear of twice the diameter. The
hypocycloid 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 pos ...
. 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
* Linkage (mechanical)
*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 tea ...
Simulations
using the Molecular Workbench software
- Hart's A-frame (draggable animation) 6-bar linkage
Linkages (mechanical)
Linear motion
Straight line mechanisms