268. In the combination of fig. 181, the screw roller will prevent the irregular heaping up of the cord on the barrel, but will not correct the varying obliquity of the cord. This may be got rid of thus. b Fig. 183. D Let B, fig. 183, be the sliding carriage, CD, HK the sides of the frame which supports the roller, E the roller formed into a screw. This roller has a screw F cut on its axis, of the same pitch as that of E, and passing through a nut in the frame CD; the other extremity of the roller is supported by a long plain axis G, passing through a hole in the frame HK; the cord being tied at b to the carriage, and at the other end to the screw-barrel E; it follows, that when the latter is turned round, it will travel at the same time endlong by means of the screw and nut F, exactly at the same rate, but in the opposite direction, as the end of the cord is carried along the barrel by its coiling; consequently the one motion exactly corrects the other, and the cord b will always remain parallel to the path of the slide B.* B H UG E a K A similar and contrary cord being employed to connect the other end of the slide with the barrel, will enable the roller to move the slide in either direction. 269. A well made chain of the common form, with oval or square links, will coil itself with great regularity upon a revolving barrel, if a spiral groove be formed upon the surface, of a width just sufficient to receive the thickness of the links. As shown in fig. 184, the links upon the sur 270. When the rotating piece is required to move only through a fraction. of a revolution, the combination is made. more simple. Thus let A, Fig. 185 represent a piece Fig. 184. or quadrant, whose axis is B, b, and whose edge is made concentric to it, and let CD be the sliding piece, represented as an open frame for clearness only, but supposed to be guided so as to move in either direction along the line CD produced. If * From a machine by Mr. Holtzapfel. cords or chains be attached at c, d, to the quadrant and at e, Fig. 185. d A B f, to the sliding frame; and a third intermediate cord be attached contrariwise to the quadrant at h and the frame at g, then either the motion of the quadrant or the frame will communicate motion to the other in a constant ratio, and in either direction at pleasure. Bands of flexible metal, e.g. of watch-spring, may be employed in cases where the flexure is small and of limited extent, as in this figure. 271. IF the varied motion is required to be limited to a small arc, the combination assumes the form of fig. 5 (page 16), but if the limits of the varied motion extend to more than a complete revolution a spiral groove is employed, as in the fusee of a watch, represented in fig. 186. Fig. 186. B Aa, Bb are parallel axes, one of which carries a solid pully, or fusee, as it is termed, upon whose surface is formed a spiral groove, extending in many convolutions from one end to the other. The axis Bb carries a plain cylinder; a band, a cord, or chain, is fastened as at m to one end of the fusee, and coiled round it, following the course of the spiral; the other end of the cord is fixed to the barrel at n. If the cord be kept tight by the action of a weight or spring upon one of the axes, the rotation of the other axis will communi b cate by means of the cord a rotation to the first axis, the velocity ratio of which will vary inversely as the perpendiculars from the axes upon the direction of the cord. And the motion may be continued through as many revolutions as there are convolutions in the spiral. In like manner a pair of fusees may be employed instead of a fusee and cylinder. 272. If the fusee be required to communicate motion in both directions without the use of the re-acting weight or spring, a double cord will answer the purpose. Thus let it be required to employ the fusee in the manner of the barrel A, fig. 181 (p. 195), to give motion to a carriage B. The fusee will enable us to obtain a varying velocity ratio between A and B. In fig. 187 Aa is the axis of the fusee, which in this example is made to diminish at both ends. One cord is fastened at m, and being coiled round the fusee is carried away at n, and attached to the carriage, as at c, fig 181. The other cord is fixed at p to the fusee, and being coiled in the opposite direction, leaves the fusee at the same point at which the first cord is carried off. But this cord is taken in the opposite direction, as at q, and fixed to the end d (fig. 181) of the carriage (or, which is better, both cords are carried over pullies and brought back to the carriage). When the axis Aa revolves, one cord will unwrap itself from the fusee, while the other wraps upon it, and vice versâ. But they will always leave its surface in opposite directions at the same point. Since the fusee (fig. 187) is small at each end and large in the middle, it will, if turned with a uniform angular velocity, have the effect of gradually accelerating the motion of the carriage, till it has reached the middle of its path, and then of gradually retarding it to the end. It is employed in this manner in the self-acting mule of Mr. Roberts, of Manchester. CHAPTER X. ELEMENTARY COMBINATIONS. DIVISION C. COMMUNICATION OF MOTION BY WRAPPING CONNECTORS. CLASS C. VARYING VELOCITY RATIO AND CONSTANT OR VARYING DIRECTIONAL RELATION. 273. THIS is obtained by employing circular or curvilinear pullies revolving about excentric centers. The diagrams which follow represent my apparatus by which these transformations of motion can be effected, and exhibited in the lecture room. Fig. 188. C is a plain circular disk fixed to the end of an axis A, which is mounted in a socket carried by a vertical board or frame, so as to leave the face of the disk perfectly free. A handle at the hinder end of the axis enables it to be rotated at pleasure. prs is a smaller disk of curvilinear outline, having an angular groove sunk round its circumference in the manner of a pully. This, from its form, may be termed a cam pully. A simple thumb-screw at the back is arranged so as to enable this cam pully to be secured against the face of the disk in any required position W as shown in the figures. In fig. 188 the center of rotation of the disk is contained within the circumference of the cam pully. In figure 189 the cam pully is fixed to the disc in a position beyond the center. In fig. 190 the center of rotation of the disc touches the circumference of the cam pully. B is a plain circular |