A Treatise on the Theory of Screws

Forfatter: Sir Robert Stawell Ball

År: 1900

Forlag: The University Press

Sted: Cambride

Sider: 544

UDK: 531.1

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31] SCREW CO-ORDINATES. 33 30. The Intensity of the Resultant may be expressed in terms of the intensities of its components on the six screws of reference. Let a be any screw of pitch pa, let p„ p2, Szc. p6 be the pitches of the six screws of reference &>1; co,, ... coe; then taking each of the screws of refer- ence in succession, for y in § 29, and remembering that the virtual coefficient of two coincident screws is simply equal to the pitch, we have the following equations:— = a/'pi + a2"OTi2 + ... + a6"’w16, a"wB8 = + ... + «6"wM4- ae"pe. But taking the screw p in place of y we have Ct pa Ot j ^"«6 • Substituting for wal ... wall from the former equations, we deduce paa"s = 2 (jpi«/'2) + 22 (ai"«2"w12). This result may recall, the well-known expression for the square of a force acting at a point in terms of its components along three axes passing through the point. This expression is of course greatly simplified when the three axes are rectangular, and we shall now show how by a special disposition °f the screws of reference, a corresponding simplification can be made in the formula just written. 31. Co-Reciprocal Screws. We have hitherto chosen the six screws of reference quite arbitrarily; we now proceed in a different manner. Take for co,, any screw; for w2, any screw reciprocal to cop, for