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Now as the trainarm, T, is carried round, the cranks, B and C, will turn in their bearings; but by their connection with A, they are compelled to remain always parallel to themselves, and thus the axis of the moon receives a motion of translation.

The planetary body is carried round by a trainarm, and its rotation about its axis is usually given it by a train of gearing, the inner or central wheel of which is stationary, being fastened to the fixed frame supporting the whole.

The mechanism consists of a trainarm, T, which turns upon the vertical pivot, P, fixed in the stand.

N, the point D a circle, and S an ellipse; C D being the trainarm.

It makes no difference what the actual value of the ratio A/_a_ may be, but it must be equal to F/_f_: under which condition it is evident that if A and F be driven contrary ways at equal speeds, small or great, the trainarm will remain at rest; but any inequality will cause the index to turn.

In these the velocity ratios are constant, if we except the cases in which two independent trains converge, the two sunwheels, or one of them and the trainarm, being driven separately  and even in those, a variable motion of the ultimate follower is obtained only by varying the speed of one or both drivers.

The same object may also be accomplished as shown in Fig. 34, the index being carried by the trainarm.

In Fig. 33, an index, P, is carried by the wheel, F: the wheel, A, is loose upon the shaft of the trainarm, which latter is driven by the wheel, E.

In some cases, particularly when annular wheels are used, the trainarm may become very short, so that it may be impossible to mount the planetwheel in the manner thus far represented, upon a pin carried by a crank.

Then, as the trainarm revolves, the three cranks must remain parallel to each other; but C D being fixed, the cranks, H F and B G, will remain always parallel to their original positions, thus receiving the required motion of circular translation.
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