516 PROFESSOR R. H. SMITH ON A NEW GRAPHIC 



evidently the method of finding the velocity pc of the block is to draw from a 

 and b two lines parallel to the two slots in A and B. If these lines meet in c, 

 then pc is the velocity required. 



If the slotted bars have rotational instead of purely translatory velocities, 

 then precisely the same construction is to be followed, making pa and pb the 

 linear velocities of the touching points of the guide-surfaces in A and B. Now, 

 however, it is evident that one and. the same block cannot constantly fit close 

 to both slotted guide-surfaces. But if two fitting blocks, one fitting the one 

 slot and the other the other, be pinned together, then the above construction 

 may be applied to find the velocity of the centre of the joining pin, and from 

 the velocity of this centre it is easy to deduce by methods already explained 

 the velocities of all other points in the two sliding blocks. 



These last graphic methods have been applied to the calculation of velocity 

 and acceleration diagrams for Player's pneumatic forging hammer, in which a 

 combination of oscillating sleeves, through which slide levers, makes the com- 

 plexity of the mechanism such as to be incapable of algebraic treatment in a 

 manner that is at once accurate and yet not impracticably cumbersome. 



The following application (see fig. 10) of the construction for sliding motion 

 to toothed wheel gear well illustrates the complete generality of the method, 

 and owes its interest not chiefly to its technical character. 



The sketch represents four wheels, P A A, PbBu P b B 2 and P C C, pinned to the 

 base-plate at P A , P B , and P c . The point A of the first touches the point B, in 

 the second, the two surfaces having here a common tangent to which the 

 line (AB^Tab is drawn normal. The third wheel being mounted on the same 

 shaft as the second, these two are to be looked upon as forming, along with the 

 shaft, one bar of the mechanism. The third and fourth wheels touch at the 

 common point (B 2 C), and the line (B,C)T BC is drawn normal to the common 

 touching surface. The points T AB and T BC are in the centre lines P A P B 

 and P B P C . 



The velocity of the wheel A, and therefore of its touching point A, is 

 supposed known, and this velocity is marked off as pa from any pole p, the 

 the line pa being drawn perpendicular to P A A. Then pb x and ab t intersecting 

 in bi are drawn perpendicular to P B B, and to B^b. This gives pb x the velocity 

 of B! and ab x the velocity of sliding of one tooth over the other. 



Then pf>. 2 and bjx, intersecting in b 2 are drawn perpendicular to P B B 2 and to 

 B,B 2 ; pb. 2 is the velocity of the point B 2 . Finally, pc and b t c intersecting in c 

 are drawn perpendicular to P C C and to the normal CT BC . This gives pc the 

 velocity of C, and b 2 c the sliding velocity of this second pair of teeth over each 

 other. The process may be carried on indefinitely through a whole train of 

 wheel work, however complicated. As a method of finding the velocities 

 throughout such a train, however, it is not a practically useful one, because the 



