ANALYSIS OF THE KINEMATICS OF MECHANISMS. 515 



any one direction inclined to S), and through the two points thus obtained a 

 straight line is drawn to cut the line 8 in the true position of d . From d or 

 b' thus determined, the other points are constructed as usual. 



This indirect method of "two trials and two errors," and linear interpolation 

 between them, is adopted in drawing the velocity and acceleration diagrams for 

 the ordinary steam-engine reversing link motion. These diagrams could not be 

 obtained except by this method. It may be mentioned that this is frequently 

 the only practicable method by which stress-diagrams of immovable linkworks 

 can be completed. 



In the common steam-engine mechanism we have already had a case of one 

 bar sliding on another, namely, the cross-head sliding in the guide-bars of the 

 bed-plate. A circular slot in which sliding takes place may, of course, be 

 looked upon as simply an incomplete pin joint of large size, the radius of the 

 pin becoming infinite when the slot is straight. But when the radius of the 

 slot is large, this manner of regarding the joint is not practically useful. A 

 more direct application of the present graphic method to sliding joints is 

 effected thus : If B be a bar sliding over the bar A, the difference of the 

 velocities of any two touching points in B and A is a velocity parallel to the 

 slide-surface, or "guide-surface." 



Thus, the velocity of the bar A being known, the velocity of any point in B 

 can be obtained by adding to the velocity of any touching point in A a velocity 

 parallel to the guide-surface, and further adding a velocity perpendicular to the 

 line joining this touching point with the point in B whose velocity is to be 

 found. 



This last added component is that due to the rotation of B in the field of 

 the base-plate. If the touching surface of B has the same shape as that of A, 

 so that B always " fits " on to all parts of A into contact with which it comes, 

 and if during the sliding these fitting surfaces are forced always to lie close 

 together, then the angular velocity of B is always the same as that of A. In 

 this case, if the velocity of A be completely known, the linear velocity of any 

 point in B can be calculated by adding to the velocity, which the point would 

 have if B wers rigidly attached to A, a velocity parallel to the guide-surface. 



In the illustration (fig. 8), the velocity of point A round P x is supposed to be 

 known, and it is plotted as pa. Then pfi and a/3 are drawn perpendicular to 

 P3 and AB. This gives pfi the velocity that point B would have if the cross- 

 head were rigidly attached to the guide-bars, and if /36 be drawn parallel to the 

 slot, the point b must lie in this last line. But B is guided by the radius rod 

 PoB. Therefore pb is drawn perpendicular to P 2 B to meet fib in b ; then pb is 

 the velocity of B in the P field, and (3b is the velocity of sliding in the slot. 



If a block C (see fig. 9) slide in two slotted bars A and B, the first of which 

 has a translatory velocity pa, and the second a translatory velocity pb, 



VOL. XXXII. PART III. 4 Q 



