300 APPLIED SCIENCE 



giving the complete diagram of Fig 17 a. The diagram Fig. 17c 

 will help to explain the significance of the several links. The 

 element d, which is the bed-plate, is here shown by itself; it is 

 in equilibrium under four external forces, indicated by arrows 

 numbered as the links in the frame are numbered ; and as this 

 plate is itself in equilibrium, the resultant of 1 and 3 will be 

 opposite and equal to the resultant of 5 and 6. The forces at 

 the joints may therefore be represented by the stresses in the 

 four half links, 1, 5, 6, and 3, joined as in the diagram by a link 

 4, in which the stress will be that due to the resultant of 1 and 

 3, or 5 and 6. The frame, if drawn on the hypothesis of no 

 friction, will be kinematically equivalent to the actual engine J 

 that is to say, the infinitesimal compression of link 6, resulting 

 from a given infinitesimal expansion of link 1, will be equal in 

 length to the actual travel of the fly-wheel at its rim past the 

 friction-block, when the piston advances by an amount equal to 

 the given expansion of link 1. The diagram, independently of 

 its value as a means of estimating the relation between effort 

 and resistance, is of use in showing clearly the direction and 

 magnitude of the stresses to which the bed-plate is subject. 

 As the revolution of the crank continues the dynamic frame 

 changes. Figs. 17 to 20a show four positions of the engine 

 with four dynamic frames ; the bearing-points are marked in 

 each case by dots on the circles representing sections of the 

 pins. The changes in the direction of the stress in the con- 

 necting rod, relatively to its axis, should be observed, as well as 

 the sudden changes which take place in the points of bearing 

 pressure as the crank-shaft revolves. It is these sudden changes 

 which give rise to ' knocks ' in the engine when the shafts or 

 pins and bearings or eyes do not fit. At joint ab four sudden 

 changes occur two due to changes of relative motion between 

 the pin and eye, and two to changes in the direction of the 

 stress in the link ; at joints be and cd there are only two 

 changes. It must be understood that the whole dynamic frame 

 is modified by any change in the direction or position of the 

 resisting link. It will be found easy to construct diagrams 

 showing the modifications resulting from a change of this kind 

 or from the substitution of a couple between c and d for the 

 resisting link ; this latter case corresponds to the arrangement 



