# Straight-Line Mechanism

## straight-line mechanism

[′strāt ¦līn ′mek·ə‚niz·əm]
(mechanical engineering)
A linkage so proportioned and constrained that some point on it describes over part of its motion a straight or nearly straight line.

## Straight-Line Mechanism

a mechanism in which all or part of the trajectory of a point on some member performing a complicated motion maintains either a rectilinear path or a curved motion that deviates little from a straight line. The linear motion is achieved not by means of special linear guides but by a selection of ratios between the lengths of the mechanism’s members.

The best-known straight-line mechanisms are those designed by P. L. Chebyshev and J. Watt. Both are pivoted four-bar mechanisms; that is, they consist of four members that form turning pairs with each other. If the length of the fixed member in a Chebyshev straight-line mechanism is assumed to be 1 and the length of the connecting rod opposite the fixed member is designated by r, then the two other members that adjoin the fixed member will have the same length, represented by l = 1.5 - 0.5 r. Here, r lies within the range from 0.333 to 0.643. When these ratios are satisfied, the point located in the middle of the connecting rod describes over part of its motion a path that differs little from a straight line. For example, in a path that is 100 mm long, the deviation from linearity amounts to no more than 0.1 mm. Chebyshev’s work in selecting the dimensions for the straight-line mechanism has formed the basis for the mathematical theory of the best approximation for functions.

Straight-line mechanisms are used, for example, in recorders to effect the linear motion of the recording pen and in certain automatic machines to govern the motion of operating elements that have periodic stops of specified duration. In the latter case, two members are added with one translational and two rotating pairs such that during the motion of the tracing point along a straight line the output (working) member is left motionless.

N. I. LEVITSKII

## Straight-line mechanism

A mechanism that produces a straight-line (or nearly so) output motion from an input element that rotates, oscillates, or moves in a straight line. Common machine elements, such as linkages, gears, and cams, are often used in ingenious ways to produce the required controlled motion. The more elegant designs use the properties of special points on one of the links of a four-bar linkage. See Mechanism

Four-bar linkages that generate approximate straight lines are not new. In 1784 James Watt applied the concept to the vertical-cylinder beam engine. By selecting the appropriate link lengths, the designer can easily develop a mechanism with a high-quality approximate straight line. Contemporary kinematicians have contributed to more comprehensive studies of the properties of the mechanisms that generate approximate straight lines. The work not only describes the various classical mechanisms, but also provides design information on the quality (the amount of deviation from a straight line) and the length of the straight-line output. See Linkage (mechanism)

Gears can also be used to generate straight-line motions. The most common combination would be a rack-and-pinion gear. See Gear

Cam mechanisms are generally not classified as straight-line motion generators, but translating followers easily fall into the classical definition. See Cam mechanism

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