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I.—On the Application of Graphic Methods to the Determination of the Efficiency of Machinery

Published online by Cambridge University Press:  14 March 2016

Fleeming Jenkin
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Extract

The object of the present paper is to show how, by graphic methods, we may find the relation between the effort exerted at one part of a machine in motion, and the resistance overcome at another part; the solution found is rigorous for all motions in one plane, and takes count of the friction, weight, and inertia of the parts. It also takes into account the stiffness of ropes or belts.

The paper shows that we may represent any machine, at any given instant, by a frame of links, the stresses in which are identical with the pressures at the joints of the machine. This self-strained frame is called the dynamic frame of the machine, and may be so drawn as to represent the machine either rigorously, taking into account friction, weight, inertia, and rigidity, or approximately, omitting some of the conditions under which the machine works.

Moreover, it is shown that for all machines (in which the motions can be represented as in one plane), the dynamic frame is of one type, either simple or compounded. The dynamic analysis of machinery into parts represented by this simple frame is believed by the author to be novel. It is consistent with the kinematic analysis of Reuleaux.

Type
Research Article
Information
Earth and Environmental Science Transactions of The Royal Society of Edinburgh , Volume 28 , Issue 1 , 1877 , pp. 1 - 35
Copyright
Copyright © Royal Society of Edinburgh 1876

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References

page 7 note * The writer has in this paper ventured to use the verb “to replace” as it is usually employed by writers on chemistry, namely as the translation of the French word “remplacer.”

page 8 note * In this frame it might be necessary to include at least one stiff bar or frame to meet opposite and equal couples.

page 11 note * Vide J. Clerk Maxwell on Reciprocal Figures, Phil. Mag. April 1864; and Jenkin, Fleeming, Trans. Roy. Soc. Ed. vol. xxv. 1869 Google Scholar.

page 13 note * In the frame of the machine shown in fig. 45, Plate XII., links 1 and 6 might be drawn so as to appear adjacent, by placing link 4 so as to join the intersection of 1 and 6 with that of 2 and 5. The links 2, 3, 5, do not, however, in this example, form a stiff frame, and the machine belongs to class 1. This is obvious when link 4 is placed so as to join the intersection of 1 and 5 with that of 2 and 6. Machines of class 2 have only 5 working joints.

page 16 note * When the method of reciprocal figures is used to find the stresses in the links, it will he necessary in all cases to substitute a stiff frame of 3 links for the bars shown in the diagrams.

page 19 note * The steam, piston, and cylinder constitute, with the resisting link, a simple inclined plane machine, vide § 15, and this machine drives the second machine, constituted by the piston rod, connecting rod, crank, bed plate, and resisting link; the piston rod and bed plate are common to the two machines, vide § 24, 25.

page 20 note * If, however, there were a joint between these parts, such that the pressure from the guide bars must pass very near the centre of the pin at that joint, then links 5 and 2 would be first drawn, and link 1 drawn cutting their dynamic joint; this arrangement would cause the effort exerted by the piston to pass a little way from the axis of the cylinder, as shown in fig. 17b.