By Dalby William Ernest
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Extra resources for The Balancing of Engines
Having selected the position of these two planes, choose one of THE BALANCING OF REVOLVING MASSES. them by for a reference plane. the three masses masses balancing (1) be zero (2) Let The sum it that 31 Then the conditions to be fulfilled the disturbing mass and the two is, are of the forces at 0, the supposed fixed point, must ; The sum of the centrifugal couples M (Fig. must be zero. 28) be the mass to be balanced, by masses placed Fir, in planes Nos. reference plane, I. and II. respectively.
Checking the Accuracy of the Work. Having balancing masses, add them to the drawing positions relatively to the given masses plane anywhere, and draw a If it close, it the work. The is ; in choose a found their new the proper reference new couple polygon relatively to it. no mistake has been made in the same for all positions of the safe to infer that force polygon is reference plane. 29, Nomenclature, It will be noticed that each term in the THE BALANCING OF ENGINES. 36 brackets of equation (2), Art.
If a pair of ratios are equal, the corresponding masses are in the plane of revolution. same is, This principle shows that two masses cannot balance one another unless they are in the same plane of revolution, for the only pair of polygons which can be drawn are a pair of lines and aba, in which the ratio returning on themselves, ABA AB ab = BA : Assuming : la three masses to be in balance, let FIG. 42. (Fig. 42) FIG. 43. be the force polygon, in this case a triangle. as ale (Fig. 43), can be ABC drawn with No other triangle, "parallel sides unless it be THE BALANCING OF REVOLVING MASSES.
The Balancing of Engines by Dalby William Ernest