. The Civil engineer and architect's journal, scientific and railway gazette. Architecture; Civil engineering; Science. ISoO.] THE CIVIL ENGINEER AND ARCHITECT'S JOURNAL. 133 centres of rotationâO anil F, slioulcl continue in contact without any other than a rolling; motion one on another, appear to be, tliat if we assume any two points, B and C, such that the arcs AB, AC,. measured from the original point of contact A along the periphery of each curve, be equal in length: 1st. Tlie sum of the vectors FC, OB, must be equal to FO; and, 2nd. That the sum of the angles FCII, OBK, made by the vec-
. The Civil engineer and architect's journal, scientific and railway gazette. Architecture; Civil engineering; Science. ISoO.] THE CIVIL ENGINEER AND ARCHITECT'S JOURNAL. 133 centres of rotationâO anil F, slioulcl continue in contact without any other than a rolling; motion one on another, appear to be, tliat if we assume any two points, B and C, such that the arcs AB, AC,. measured from the original point of contact A along the periphery of each curve, be equal in length: 1st. Tlie sum of the vectors FC, OB, must be equal to FO; and, 2nd. That the sum of the angles FCII, OBK, made by the vec- tors with tangents at the points B and C, must be equal to x, or 180°. For unless the first of these conditions be fulfilled, it appears plain, that when, by the motion of the axis at O, the one curve shall have assumed the position represented by the dotted periphery, the point B having been brought to the position B', the point C would not be, as it should be, in contact; and if the second were not fulfilled, the curves would intersect at some other point, instead of having a common tangent at B'. I need not take up your valuable space by entering into any detailed proof that these conditions are fulfilled by equal and similar ellipses working on foci, as a very slight acquaintance with the properties of the ellipse is suflicient to show tliat such is the case. That they may not possibly be fulfilled by some other more complex curves, I do not venture to assert, as the problem would be one of such extreme intricacy witli regard to any other than equal, similar, and symmetrical forms; but I do not regard it as probable that any such curves can be found. This principle would enable us to obtain motions of rotation of different degrees of variatiuii, but of the same characterâviz. with one maximum and one minimum velocity in the course of eacli revolution, according to the excentricity of the ellipses made use of. The revolution of the one wheel is necessarily conterminous
Size: 2059px × 1213px
Photo credit: © The Book Worm / Alamy / Afripics
License: Licensed
Model Released: No
Keywords: ., boo, bookcentury1800, booksubjectarchitecture, booksubjectscience
