An elementary course of infinitesimal calculus . Fig. 107. Hence if P (or Q) be made to describe any curve, Q (or P)will describe the inverse curve with respect to 0. In particular if, by a link, P be pivoted to a fixed point 8,such that SO = SF, the locus of P is a circle through 0, andconsequently the locus of Q will be a straight line perpendicularto OS. This gives an exact solution of the important mechanicalproblem of converting circular into rectilinear motion by meansof link-work. 2°. Harts Linkage. This consists of a crossed parallelogram A BCD formed H--. Fig. 108. 382 INFINITESIMAL C
An elementary course of infinitesimal calculus . Fig. 107. Hence if P (or Q) be made to describe any curve, Q (or P)will describe the inverse curve with respect to 0. In particular if, by a link, P be pivoted to a fixed point 8,such that SO = SF, the locus of P is a circle through 0, andconsequently the locus of Q will be a straight line perpendicularto OS. This gives an exact solution of the important mechanicalproblem of converting circular into rectilinear motion by meansof link-work. 2°. Harts Linkage. This consists of a crossed parallelogram A BCD formed H--. Fig. 108. 382 INFINITESIMAL CALCULUS. [CH. IX of four rods jointed at their extremities, the alternate sidesbeing equal. A point 0 in one side AB is made a fixedpivot, and P, Q are points in AD and BG such that AP : PD=GQ • QB = AO : OB, = m : w,say. Evidently 0,P, Q will lie in a straight line parallel to ^Cand BD. If H, K be the orthogonal projections of J., C onBD, and if N be the middle point of BD, we have = 2NH. 2NB = DH^ - BH = AD- AB\ Now OP:BI) = AO:AB = m:m + n, and OQ:AG = BO:AB = n:m + n. Hence , ^^ .,(AD - AB) = const (2). Hence P and Q describe inverse curves with respect to 0. As before, by connecting P to a fixed pivot jS by a link PSequal to SO, we can convert circular into rectilinear motion. 147. Pedal Curves. If a perpendicular OZ be drawn from a fixed point 0 onthe tangent to a curve, the locus of the foot Z of thisperpendicular is called the pedal of the original curve withrespect to the origin 0. Thus : the pedal of a parabola with respect to the
Size: 1972px × 1267px
Photo credit: © The Reading Room / Alamy / Afripics
License: Licensed
Model Released: No
Keywords: ., bookcentury1900, bookdecade1900, bookpublishercambr, bookyear1902
