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Roberts Linkage.Links of the same color are the same length.
Roberts Linkage.
Links of the same color are the same length.
Sarrus Linkage.Parts of the same color are the same dimensions.
Sarrus Linkage.
Parts of the same color are the same dimensions.
Peaucellier-Lipkin Inversor.Links of the same color are the same length.
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.[citation needed]


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 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.[citation needed]

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.

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.

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.


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


  1. ^ a b c d e f g h i Linkage has unstable positions that are not accounted for. Mitigations for said unstable positions are not shown for the sake of clarity.


  1. ^ Kempe, Alfred Bray (1877). How to Draw a Straight Line: A Lecture on Linkages. Macmillan and Company. ISBN 978-1-4297-0244-7.
  2. ^ Artobolevsky, Ivan Ivanovich. Mechanisms in modern engineering design. ISBN 978-5-9710-5698-0.
  3. ^ Four-cylinder, Four-cycle Engine With Two Reciprocating Components, A.J.S Baker, M.E Cross, The Institution of Mechanical Engineeers, Automobile Division, Volume 188 38/74
  4. ^ Parsons' epicyclic engine
  5. ^ Clean engines - A combination of advanced materials and a new engine design