Straight-line mechanism

An animation of Watt's Linkage.
An animation of Roberts Linkage.
Sarrus Linkage.
Parts of the same color are the same dimensions.
Peaucellier-Lipkin Inversor.
Links of the same color are the same length.

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, 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, 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, for guiding the pistons 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 were not as needed, as by then other techniques for machining had been developed.

List of linkages

Approximate straight-line linkages

These mechanisms often use 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 perfect straight-line motion using a four-bar linkage, without using a prismatic joint.

Perfect straight-line linkages

Eventually, perfect straight line motion was 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 uses 6-bars–and the quadruplanar inversors–Sylvester-Kempe and Kumara-Kampling, which also use 6-bars.

The Scott Russell linkage (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.

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.

  • Trammel of Archimedes. Originally an ellipsograph. Also known as the double-slider 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.[3] It has been used in inverted form in Parsons' steam engine[4] and can still be found today in further inversions as the Oldham coupling and the scotch yoke mechanism.
Stiller-Smith eccentric gear train, core features.[5]
MultiFAZE[6] eccentric gear train for a 3-cylinder radial engine.[7]
  • The Stiller-Smith Mechanism is a compound eccentric mechanism that combines a double-slider mechanism with a novel eccentric gear train consisting of a set of spur gears of equal size. It converts reciprocating motion to rotary motion and vice versa using the rotary component of the elliptical motion instead of the orbital or circular component.[8] Patent No. DE 3232974 published in March 1984 gives Michael Mayer as the inventor of the eccentric gear train aka MultiFAZE[6] mechanism, and describes several embodiments of the gear train in piston engines including a cruciform engine. A provisional patent application (See Patent No. US 4641611) filed by West Virginia University (USA) in July 1984 gives Profs. Alfred H. Stiller and James E. Smith as joint inventors of the eccentric gear train, without citing the Mayer patent.
    The difference between the two mechanisms is that in the Stiller-Smith version, a "floating trammel gear" (Fig. 16, Part No. 426) functions as a cantilever that links two piston rods reciprocating in perpendicular directions, in a floating kinematic chain, while in the earlier Mayer version, an "orbital shaft" (Fig. 4, Part No. 10) is supported at both ends such that it is given circular or orbital motion.
    Variants of the Stiller-Smith Mechanism to be found in the West Virginia University patents include one with a toothed belt drive instead of gears and one with a combined belt and gear drive, with the belt around the intermeshed input and output gears.[9] The mechanism was used in two experimental 4-cylinder cruciform engines designed and built at West Virginia University, accompanied by much publicity.[10][11] 175 companies signed non-disclosure agreements to be able to view the engine.[12] Vice-President George Bush visited West Virginia University on 3 May 1988 to see research work including the Stiller-Smith engine project.[13]
    Stiller recounts that he had for some time been fascinated by a “do-nothing machine”, a toy based on the double-slider mechanism, and was sure it could be used in an engine.[14]. The Baker-Cross IC-engine of 1974[3] and Parsons' steam engine of 1877[4] both used a double-slider crank mechanism.
    In an interview in 1987, Smith mentions a gear train with two gears that converts the reciprocating motion of the pistons to rotary motion, and praises Stiller as a remarkable inventor.[12] In an interview in 1988 he discloses full details of the eccentric gear train, and explains that he got the idea from a Spirograph, a toy for drawing patterns that uses a fixed ring gear and a moving spur gear, while the eccentric gear train has only spur gears, all of which move. He points out that the gear train is the central feature of the Stiller-Smith mechanism.[15]
    Smith et al. used elaborate mathematical calculations to derive parameters for an eccentric gear train, but with equivocal results, so that, in the end, practical considerations determined the configuration of the gear train.[16] The paper does not explain how the characteristics of the gear train match the input and output motions of an engine with a double-slider mechanism. The Stiller-Smith Mechanism became the subject of Prof. Smith's dissertation[17] and kick-started his career.
    The engine was expected to be suitable for the use of ceramic materials to achieve adiabatic combustion[8][18] at much higher temperatures than in conventional engines, which would enable the use of heavy fuels if diesel fuel was scarce. This, and the prospect of a high-performance engine for heavy vehicles, raised the interest of the Army which awarded the University a million-dollar development contract, as reported in 1987.[15] However, most of the work was theoretical, centring on computer simulations and analyses of the kinematics and expected forces and loads in the mechanism, which spawned a string of technical reports and conference papers.[19]
    On 13 November 1989 the US Congress approved a grant of $1,760,000 for research by the Army into the engine's potential for future combat vehicles.[20]

Approximate straight-line linkages

Parts/links of the same color are the same dimensions.

Perfect straight-line linkages

Parts/links of the same color are the same dimensions.

Tusi couple, elliptical motion: versions and inversions

Compound eccentric mechanisms with elliptical motion

See also

Notes

  1. 1 2 3 4 5 6 7 8 9 Linkage has unstable positions that are not accounted for. Mitigations for said unstable positions are not shown for the sake of clarity.

References

  1. ↑ Kempe, Alfred Bray (1877). How to Draw a Straight Line: A Lecture on Linkages. Macmillan and Company. ISBN 978-1-4297-0244-7. {{cite book}}: ISBN / Date incompatibility (help)
  2. ↑ Artobolevsky, Ivan Ivanovich. Mechanisms in modern engineering design. ISBN 978-5-9710-5698-0.
  3. 1 2 Four-cylinder, Four-cycle Engine With Two Reciprocating Components, A.J.S Baker, M.E Cross, The Institution of Mechanical Engineers, Automobile Division, Volume 188 38/74
  4. 1 2 "Dampfmodellbau". www.dampf.gniephaus.de. Retrieved 2026-08-23. and Patent Nos. GB2344(?) and GB4266
  5. ↑ From Patent No. US 4641611. See also publications by J. Smith et al, e.g. Complete Balancing of the Stiller—Smith Engine: 4, 8, 12, 16 or More Cylinders
  6. 1 2 Acronym for Multiple Fixed Axis Shaft Compound Eccentric
  7. ↑ From Patent No. DE 3232974
  8. 1 2 Clean engines - A combination of advanced materials and a new engine design, James E. Smith, Randolph A. Churchill, Jacky Prucz, West Virginia University, 1988
  9. ↑ Patent No. US 5046459, Claim 2
  10. ↑ WVU professors design revolutionary engine, UPI Archives
  11. ↑ Chemical Engineering at West Virginia University: A Living History, p. 79.
  12. 1 2 Automotive News 20 April 87
  13. ↑ PR Newswire Association, Inc. 1988-04-28
  14. ↑ Mineral Daily News Tribune, Page9, 1984-08-16
  15. 1 2 Pittsburg Post Gazette 2 May 1988
  16. ↑ The Stiller-Smith mechanism: a kinematic analysis, James E. Smith, Robert P. Craven, and Robert G. Cutlip, West Virginia University. Paper for the International Congress and Exposition, Detroit, February 1986. The paper is available from SAE International for $39 to non-members.
  17. ↑ Smith, James E. "The dynamic analysis of an elliptical mechanism for possible application to an internal combustion engine with a floating crank". Dissertation. West Virginia University. 1984.
  18. ↑ The Stiller-Smith Engine - The Dewelopment (sic) of a New Environment for High-Tech Materials
  19. ↑ See, for example, Researchgate(1) and Researchgate(2)
  20. ↑ November 13, 1989 CONGRESSIONAL RECORD - HOUSE Vol. 135 Part 20, P. 28453
  • Theory of Machines and Mechanisms, Joseph Edward Shigley
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