Descriptive geometry . e-stricting the motion of the generatrix. Any warped surface may be generated by arectilinear generatrix moving so as to touchtwo linear directrices, and having its consecu-tive positions parallel either to a given plane,called a plane director, or to the consecutiveelements of a conical surface, called a conedirector. loi. The following types, illustrated byFigs. 142 to 148, indicate the characteristicfeatures of warped surfaces : Hyperbolic Paraboloid, Fig. 143. Tworectilinear directrices and a plane director, orthree rectilinear directrices. Conoid, Fig, 144. One rect
Descriptive geometry . e-stricting the motion of the generatrix. Any warped surface may be generated by arectilinear generatrix moving so as to touchtwo linear directrices, and having its consecu-tive positions parallel either to a given plane,called a plane director, or to the consecutiveelements of a conical surface, called a conedirector. loi. The following types, illustrated byFigs. 142 to 148, indicate the characteristicfeatures of warped surfaces : Hyperbolic Paraboloid, Fig. 143. Tworectilinear directrices and a plane director, orthree rectilinear directrices. Conoid, Fig, 144. One rectilinear and onecurvilinear directrix and a plane director. Cylindroid, Fig. 145. Two curvilineardirectrices and a plane director. Right Helicoid, Fig. 146. Two curvi-linear directrices and a plane director. Oblique Helicoid, Fig. 147. Two curvi-linear directrices and a cone director. Hyperboloid of Revolution, Fig. curvilinear directrices and a cone direc-tor, or three rectilinear directices. WARPED SURFACES 69. Fig. 147. 70 DESCRIPTIVE GEOMETRY 102. A Surface of Revolution, Fig. 149, istlie locus of any line, or generatrix, the posi-tion of which remains unaltered with referenceto a fixed right line about which it fixed right line is called the axis of revo-lution. A circle of the surface generated byany point of the generatrix is called d parallel.,and planes perpendicular to the axis will cutthe surface in parallels. Any plane contain-ing the axis of revolution is called a merid-ian plane^ and the line cut from the surfaceby this plane is called a meridian line. Allmeridian lines of the same surface are obvi-ously identical, and any one of them may beconsidered as a generatrix. That meridianplane which is parallel to a coordinate planeis called the principal meridian. If the generatrix be a right line lying inthe same plane as the axis, it will either beparallel with it or intersect it ; in the formercase the surface generated will be a cylinder,in the
Size: 1926px × 1298px
Photo credit: © The Reading Room / Alamy / Afripics
License: Licensed
Model Released: No
Keywords: ., bookcentury1900, bookdecade1900, booksubjectgeometrydescriptive
