MIT RadLab {complete set} Vol 27 - Computing Mechanisms, by A. Svoboda, H. James

By A. Svoboda, H. James

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Extra info for MIT RadLab {complete set} Vol 27 - Computing Mechanisms, Linkages

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From a practical point of view, the pure sinusoidal form is reached for links short enough for practical use. In the limiting case, L = w, the equation of the harmonic transformer is X,= Rsin Xl+C. ” Only rarely is the complete range of motion of a harmonic tra~former used. When the range of the parameter X, is limited to Xl~ < X, < Xl.. and the functions defined within these restricted limits are taken as elements of a new functional field, there is obtained a four-dimensional functional field depending on Xl~ and Xl,, as well as on L/R and E/R.

Ki > 1). ”) = lCi(Zilf – Z\O))j Xi. ol); (20a) (k< 1) (20b) then Hi~fi=l_hi. (ki < 1). (21) Equation (19) will be referred to as the “direct” identification of Hi with hi. 3] AN OPERATOR FORMALISM 49 changing in the same sense between minimum and maximum values which they attain simultaneously; the scale of xi is even, and increases in Equation (21) will be termed the “ comthe direction of increasing X;. of Hi and h,; it implies that the scale of Zi is plementary identification” even, and increases in the direction of decreasing Xi.

Rst becomes the input parameter of the second, and so on. The first mechanism determines an output parameter X2 as a function of the input parameter Xl: x, = +1(X1). (25a) The second mechanism determines an output parameter Xa in terms of Xz, X3 = +2(X2); (25b) the third determines an output parameter Xq in terms of X3, x, = @*(x,); (25c) and so on. The final output parameter, for example, Xq, is then determined as a function of Xl: x4 = q$,{ @,[+,(x,)]]. (26) The conventional notation of Eqs. (25) and (26) is fully explicit, but some times cumbersome.

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