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A Vector Account of Four-Piece Mechanisms

Published online by Cambridge University Press:  03 November 2016

W. R. Andress
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Extract

If four rigid rods are smoothly pivoted together at their ends to form a closed quadrilateral the system is said to form a four-link chain. Under certain conditions, five in number, it is found that the quadrilateral is freely deformable and the system is then regarded as a mechanism. Isolated systems, satisfying the necessary conditions and hence admitting deformation, have been known for some time, namely,

  • (a) the case in which the rods are coplanar and all the hinges are perpendicular to this plane;

  • (b) the general “spheric or conic-chain” in which the lines of the four hinges are concurrent;

  • (c) the case of the “Skew-isogram” discovered by Dr. G. T. Bennett.

Type
Research Article
Information
The Mathematical Gazette , Volume 27 , Issue 276 , October 1943 , pp. 149 - 154
Copyright
Copyright © Mathematical Association 1943

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References

page no 149 note * Macmillan, R. H., Math. Gazette, Feb. 1942, Vol. XXVI, No. 1, pp. 5–20 CrossRefGoogle Scholar.

page no 149 note * Rouleaux, Kinematics of Machinery. Trans, by Kennedy, Macmillan (1876), pp. 67, 327, etc.

page no 149 note ‡ Bennett, G. T., Proc. Lond. Math. Soc., vol. 13, series 2 (1914), p. 151 CrossRefGoogle Scholar.