Page:The Kinematics of Machinery.djvu/633

 NOTES.

�611

�60 (P. 552.) A model of the mechanism shown in Fig. 395, exhibited at Vienna, was placed beside a very nearly related piece, the so-called skew- diso (schiefe Scheibe). In the Bairischen Industrie und Gewerbeblatt, 1874, p. 100, Herr Schedlbauer gives a theory of the motion in this mechanism, and shows that the link e makes swinging motions which are given by the formula (r tan a) sin, in which r is the constant distance 1*6, a the angle between 1 and 2, and <o the angle of turning of the link a relatively to the fixed link /. According to this the link e would have a simple harmonic motion. The con- structive conditions of Herr Schedlbauer's mechanism are, however, somewhat different from those of Fig. 395, and of my model. He assumes the link b, carrying an element of each of the pairs 2 and 3, to be of the form C ... _L ... P^ and also that the axis of the last-mentioned prism always intersects the axis of the prism C at a constant distance from 1. This would be a mechanism having for its formula, beginning with the pair 1, (C^<7J_p_LCJLp"C") a. In the train represented in F j g> 395 the link e makes motions which only approximate to simple harmonic oscillations, and which are given by the expression

(r sin a) sin a>

�the

�-f- sin*o>

il: y be the distance of a point of e from its middle position and r length 2-4.

The difference between the two motions is very small with a small angle at a, and may be generally neglected in the cases which occur in machine practice. I mention the matter merely as another illustration of what I have already noticed in note 46, that the motion of a mechanism, or more correctly one of the motions occurring in it, has been often investigated without any examination having been made of the actual combination itself by which that motion was produced. The latter is. however, in the case before us the more important part of the problem, for we have already an immense number of trains in which an exact or approximate simple harmonic motion occurs, [I have called the latter distorted harmonic motion], while the various forms of the train (C+) have never yet received investigation.

The steam-engine of Robertson, mentioned upon p. 551, contained one detail which deserves further mention. Robertson used, namely, according to the published description, the driving mechanism shown in Fig. 451, which has occasioned no little astonish- ment. Here c is a spur-wheel driven by the wheel a not by means of teeth but by the water b held in the hollow ring of a ; or, as we should say more rightly, paired with a, for the water slides in a if the velocity of this wheel fluctuates. The water-ring b can therefore turn uniformly, although the wheel a moves with a variable speed received from the train (C+). It is claimed that the transference of motion will be very " sweet " ; at starting only a little water will be spattered about, afterwards the centrifugal force is sufficient to

R R 2

��FIG. 451.

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