Kinematic pair
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A kinematic pair is a connection between two bodies that imposes constraints on their relative movement. Franz Reuleaux introduced the kinematic pair as a new approach to the study of machines[1] that provided an advance over the motion of elements consisting of simple machines.[2]
Description
Kinematics is the branch of classical mechanics which describes the motion of points, bodies (objects) and systems of bodies (groups of objects) without consideration of the causes of motion.[3] Kinematics as a field of study is often referred to as the "geometry of motion".[4] For further detail, see Analytical dynamics.
Hartenberg & Denavit[5] presents the definition of a kinematic pair:
In the matter of connections between rigid bodies, Reuleaux recognized two kinds; he called them higher and lower pairs (of elements). With higher pairs, the two elements are in contact at a point or along a line, as in a ball bearing or disk cam and follower; the relative motions of coincident points are dissimilar. Lower pairs are those for which area contact may be visualized, as in pin connections, crossheads, ball-and socket joints and some others; the relative motion of coincident points of the elements, and hence of their links, are similar, and an exchange of elements from one link to the other does not alter the relative motion of the parts as it would with higher pairs.
Higher pairs
Generally, a higher pair is a constraint that requires a curve or surface in the moving body to maintain contact with a curve or surface in the fixed body. For example, the contact between a cam and its follower is a higher pair called a cam joint. Similarly, the contact between the involute curves that form the meshing teeth of two gears are cam joints, as is a wheel rolling on a surface. It has a
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Wrapping pair
A wrapping pair is a constraint that comprises belts, chains, and such other devices. A belt-driven pulley is an example of this pair. In this type of which is very similar to the higher pair(which is having point or line contact), but having multiple point contact.
References
- ^ Reuleaux, F., 1876 The Kinematics of Machinery, (trans. and annotated by A. B. W. Kennedy), reprinted by Dover, New York (1963)
- ^ A. P. Usher, 1929, A History of Mechanical Inventions, Harvard University Press, (reprinted by Dover Publications 1968).
- ^ Thomas Wallace Wright (1896). Elements of Mechanics Including Kinematics, Kinetics and Statics. E and FN Spon. Chapter 1.
- ^ Russell C. Hibbeler (2009). "Kinematics and kinetics of a particle". Engineering Mechanics: Dynamics (12th ed.). Prentice Hall. p. 298. ISBN 0-13-607791-9.
- ^ R. S. Hartenberg and J. Denavit (1964) Kinematic synthesis of linkages, pp 17-18, New York: McGraw-Hill.
- Hartenberg, R.S. & J. Denavit (1964) Kinematic synthesis of linkages, pp 17,18, New York: McGraw-Hill, online link from Cornell University.