CHAPTER VIII. 121. The distance between the centres of rotation of two non-circular pitch surfaces is 3". The forms of the surfaces have to be such that the angular velocity ratio transmitted is equal to 0.5, 0·6, 0·7, 0·8, 0·9, 1·0, 0·9, 0·8, 0·7, 0·6, 05 for equal angles of 15° turned through by the first wheel. If there is no sliding between the surfaces, find the forms of the two pitch lines. 1 2 122. In Harfield's gear (Fig. 373), the diameter of the driving wheel A is 2', and the centre of rotation is 6" from the centre of the wheel. The distance between the centres of rotation P, and P, is 6'. Draw the form of the rack for a half-turn of the driving wheel, and state the extreme helm angle. Find also the angular-velocity ratio between the rudder-head and driving wheel in the mean and extreme positions of the gear. Ans. Angular-velocity ratios, and 123. Motion is transmitted between two parallel shafts by two elliptic wheels. The distance between the centres is 4", and extreme velocity ratios have to be 3 and. Find the major and minor axes of the ellipses. 124. If the elliptic wheels in Q. 123 be used as a quick-return motion, as shown in Fig. 378, find the time ratio of the home to the cutting stroke. Ans. 4 approx. 125. Two circular wheels, one 4" and the other 6" diameter, rotate eccentrically about pins which are 4.5" apart. The eccentric radii of the two wheels are 1" and 2" respectively. Plot the mechanism in the position for which the larger eccentric radius is perpendicular to the line joining the centres of the wheels, and find the angular-velocity ratio between the large and small wheels in this position. Ans. 2 about. 126. Design a cam to lift vertically a moving piece at a uniform speed through 3", the return motion being also uniform and at half the speed. The diameter of the roller is ", the least width of metal round cam centre is 2", and the line of stroke produced passes through cam centre. 127. Draw a cam which has to raise a valve at a uniform rate through 6" in two-fifths of a revolution, and lower it through the same distance in one-fifth of a revolution. The valve remains at rest in the upper position for one-tenth of a revolution, and in the lower position for the rest of a revolution. The diameter of the shaft is 4", the least width of metal round shaft is 2", the diameter of the roller is, and the line of stroke produced passes through cam centre. 128. If, in Q. 127, the line of stroke is 2-5′′ to one side of the cam shaft centre, design a cam to give the same motion. cam. 129. A plane face, attached to a reciprocating piece, is acted on by a rotating In its lowest position the plane face is 2" from the cam shaft centre, and the line of stroke of the slide is 1" to one side of the cam centre. If the slider rises uniformly through 2" whilst the cam shaft rotate uniformly through 180°, find the proper shape for the acting edge of the cam. |