322 APPLIED SCIENCE 



introduction of friction. Beginning with link la in Fig. 386, we 



can draw line 5 making the stated angle with the surface of the 



guide bars, and lines L a L & which are identical with the lines of 



the same name in Fig. 37a. We must, however, subdivide L 6 in 



a new ratio, for it is clear that the line of bearing pressure 2a 



will pass over the friction circle, and so that the trial point 



where it intersects line 5 will be some distance to the right ; 2/3 



must pass under its friction circle, and the point which 2/3 must 



pass through on the left must obviously be near the bottom of 



its friction circle. Draw the line 2, joining two trial points, 



refer L 6 to the two ends of link 2, or, in other words, subdivide 



L 6 , Fig. 386, in the ratio in which L 6 subdivides link 2 ; from the 



point of subdivision in Fig. 386, draw 2 parallel to 2 in Fig. 38a. 



The intersection of 2 and 5 gives the point o. The piece c is 



held in equilibrium by four forces L c , 6a, 2/3, and the reaction 



from the bearing : the intersection of 2/3 with 6 (Fig. 38a) gives 



one point through which the loaded link 3 must pass, and our 



trial point for the other end must obviously be a little to the 



left of the friction circle at the main bearing, where the tangent 



3y3 cuts line 1, and this tangent 3/3 must be a little less steep 



than the line 3/3 in Fig. 376. The load L c is now to be subdivided 



between the two ends of the loaded link 3, the two components 



being l c and l' c the polygon of the forces in equilibrium at the 



upper right-hand end of 3 can now be drawn in Fig. 386, these 



are 2/3, ? c , Qa and 3 ; the two former are known and the directions 



of the two latter ; the polygon can therefore be drawn with the 



lines arranged in the order named, and thus the magnitude of 



6a can be determined. The problem is now solved, but if we 



wish to complete our drawing of the frame, we must rearrange 



the last drawn polygon, so that the forces in the reciprocal 



figure come in their natural order as shown by the full lines in 



Fig. 386, then finishing L c we can, as in Figs. 37ft and 376, 



complete the reciprocal figure and frame without difficulty. If 



we have chosen our trial points well, the lines of the frame will 



be tangent to the friction circles. If they cut these or do not 



touch them, we must correct our choice of the trial points until 



the desired figure is found. As the friction circles are generally 



very small, a single trial is generally sufficient for a draughtsman 



who has mastered the theory. The result is really remarkable. 



