284 APPLIED SCIENCE 



to the elasticity of the link or, in other words, the stress in the 

 link may oppose the motion of rotation of the pin in the eye 

 of the link ; in brief, the link must make the stated angle with 

 the surface of the joint. In the present example, where all the 

 joints are made by circular pins and eyes, this is readily done 

 by making the directions of the links tangent to, and on the 

 proper side of, circles drawn with their centres at the centres of 

 the pins, and having each a radius equal to r sin <, where r is 

 the radius of the pin in question, and <f) is the angle of which the 

 tangent is equal to the coefficient of friction for the surfaces in 

 question. 



These circles will, in what follows, be called friction circles. 

 The following mnemonic rules will be found useful in selecting 

 the side of the circle to which any given link must be tangent. 

 Case 1. When the link represents an element with only two 

 joints, and therefore does not end in any geometrical joint named 

 by the same letter as an element. Consider the link as termin- 

 ating in an eye which rotates on a pin fastened to the other 

 element. Mark by an arrow the direction of rotation of the pin 

 inside the eye. Mark also by an arrow the direction of the 

 force exerted by the link at the joint, then place the tangent so 

 that the force indicated by the arrow in the link appears to 

 oppose the motion of the pin. It must be remembered that the 

 arrow indicating the direction of the force exerted by the link 

 may, in the diagrams, frequently be found at the end of the link 

 furthest from the joint. Case 2. When the link ends in a 

 geometrical joint marked with the letter denoting the element 

 in which any pin is fast, then the arrow on the half link next 

 that geometrical joint must point as if opposing the motion of 

 the pin relatively to the other element. 



Fig. 5c, p. 279, shows the dynamic frame when the friction at 

 the joints has been taken into account, or, as it may be called, 

 the dynamic frame with friction. Eight friction circles are first 

 drawn, arrows are placed on the links, as in Fig. 5a, to indicate 

 whether these are in tension or compression ; the directions of 

 stress are by hypothesis known in links 1 and 6, and we easily 

 see what must be the direction of stress in the other links to 

 keep links 1 and 6 in equilibrium. We next put arrows .-it- 

 each friction circle in Fig. 5c, showing the motion of each pin 



