Straight-line mechanism

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.

Watt's linkage (1784) Watt's parallel motion (1784) Evans "Grasshopper" linkage (1801) Chebyshev linkage Chebyshev lambda linkage (1878), a cognate linkage 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 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.

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 (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.

Cardano's hypocyclic gears. Based on the principle of the Tusi couple (1247), a spur gear on a short crank 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, i.e. a straight line. The mechanism has been used in Murray'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. It has been used in inverted form in Parsons' steam engine and can still be found today in further inversions as the Oldham coupling and the scotch yoke mechanism.

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