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Astraight-line mechanism is amechanism that converts any type of rotary or angular motion to perfect or near-perfect straight-line motion, orvice versa. Straight-line motion islinear motion of definite length or "stroke", every forward stroke being followed by a return stroke, givingreciprocating motion. The first such mechanism, patented in 1784 byJames Watt, produced approximate straight-line motion, referred to by Watt asparallel 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 theplaner and themilling machine, it was extremely difficult to machine straight, flat surfaces. During that era, much thought was given to the problem of attaining astraight-line motion, as this would allow the flat surfaces to be machined. To find a solution to the problem, the firststraight-line mechanism was developed byJames 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.^{[citation needed]}

These mechanisms often usefour-bar linkages as they require very few pieces. These four-bar linkages havecoupler 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 – thepantograph – 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 aprismatic joint.

• Watt's linkage (1784)
• Watt's parallel motion (1784)
• Evans "Grasshopper" linkage (1801)
• Chebyshev linkage
• Chebyshev lambda linkage (1878), acognate linkage of the Chebyshev linkage
• Roberts linkage
• Horse-head linkage
• Hoecken linkage (1926) – requires a sliding joint

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 theinversion 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.

• 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^[1] (1875)
• Bricard inversor^[2]
• Quadruplanar inversor (1875)

TheScott Russell linkage (1803) translates linear motion through a right angle, but is not a straight-line mechanism in itself. TheGrasshopper 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 theTrammel of Archimedes.

These mechanisms use the principle of arolling curve instead of acoupler curve and can convert continuous, rather than just limited, rotary motion to reciprocating motion andvice versa via elliptical motion. The straight-line sinusoidal motion produces no second-order inertial forces, which simplifiesbalancing in high-speed machines.

• Cardan straight-line mechanism. Using the principle of theTusi couple (1247), aspur gear rolls inside an internally toothedring gear of twice the diameter. Thehypocycloid traced by any point on the pitch circle of the smaller gear is a diameter of the larger gear. The mechanism has been used inMurray's Hypocyclic Engine.

• 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 theOldham coupling and thescotch yoke mechanism.

• MultiFAZE is an acronym for Multiple Fixed Axis Shaft Compound Eccentric. This eccentric gear train mechanism has been used in the Stiller-Smith engine.

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

• 
  Watt's linkage
• 
  Watts parallel-motion linkage
• 
  Evans "Grasshopper" linkage
• 
  Roberts linkage
• 
  Chebyshev linkage
• 
  Chebyshev lambda linkage
• 
  Chebyshev table linkage
• 
  Hoecken's linkage

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

• 
  Sarrus linkage (Bars variant)
• 
  Sarrus linkage (Plates variant)
• 
  Peaucellier-Lipkin inversor
• 
  Harts inversor 1
• 
  Harts inversor 2^{[Note 1]}
• 
  Perrolatz inversor
• 
  Kempe kite inversor 1^{[Note 1]}
• 
  Kempe kite inversor 2^{[Note 1]}
• 
  Kempe kite inversor 3^{[Note 1]}
• 
  Scott Russell linkage (slider connection)^{[Note 1]}
• 
  Scott Russell linkage (connected to Peaucellier-Lipkin linkage)
• 
  Bricard inversor^{[Note 1]}
• 
  Sylvester-Kempe quadruplanar inversor 1^{[Note 1]}
• 
  Sylvester-Kempe quadruplanar inversor 2^{[Note 1]}
• 
  Sylvester-Kempe quadruplanar inversor 3
• 
  Kumara-Kampling inversor^{[Note 1]}

• 
  Tusi couple (1247) according to the diagrams in the translation of the copy of Tusi's original description: Small circle rolls within large circle.
• 
  Tusi couple according to the translation of the copy of Tusi's original description: Circles rotate in same direction, speed ratio 1:2.
• 
  Copernicus' (1473-1543) take on the Tusi couple: Direction of rotation and orbit of moving circle are equal and opposite.
• 
  Scotch yoke mechanism
• 
  Inversion No. 4
• 
  Inversion No. 5 - speed ratio 1:3
• 
  Inversion No. 6
• 
  Inside-out Tusi couple. The small circle is split into four fixed quadrants. Two 45° arcs of the large circle form the waist of the trammel.
• 
  Parsons' mechanism (1877) combines Tusi Inversion No. 2 with an Archimedes trammel. Pistons at A and C balance each other.
• 
  Oldham coupling (1821). Slotted ends of two misaligned shafts (black) are coupled by a cross piece (green). Compare with Tusi Inversion No. 4.
• 
  Kinematics of the Multiple Fixed Axis Shaft Compound Eccentric (MultiFAZE) mechanism (1982) characterised by parallelograms ABCD.

• 
  A spur gear with two teeth rolls inside a ring gear with four teeth: Archimedes, Tusi or Cardano?
• 
  Cardano's (1501-1576) hypocyclic gears: the red, green and blue pins reciprocate on diameters of the ring gear.
• 
  Three Archimedes (287~212 BC) trammels on a triangular rotor showing the circular orbit of the trammel midpoints.
• 
  MultiFAZE mechanism (1982) in a 60° X4 engine with yokes, and rotary counterweights for full balance.
• 
  MultiFAZE mechanism (1982) in a 90° X4 engine with crossheads, trammel gears, and reciprocating balance weights/sliders.
• 
  Stiller-Smith 90° X4 2T floating cantilever crank engine (1984) with MultiFAZE eccentric gear train. Wobble and overshoot exaggerated for effect.
• 
  Balandin MB4 cruciform engine with an eccentric crankshaft, 1930's. From a drawing with enigmatic flywheels and no pistons.

• Four-bar linkage
• Linkage (mechanical)
• Rigid chain actuator

• Theory of Machines and Mechanisms, Joseph Edward Shigley

• Cornell university (archived) - Straight-line mechanism models
• Alfred Kempe (1877).How to Draw a Straight Line(PDF).Macmillan – viaUniversity of California at Irvine.
• Daina Taimina."How to Draw a Straight Line - a tutorial".Cornell University.
• Simulations using the Molecular Workbench software
• bham.ac.uk - Hart's A-frame (draggable animation) 6-bar linkage

• Linkages (mechanical)
• Linear motion
• Straight line mechanisms

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