32 ELEMENTS OF LABORATORY WORK 



movement of a wheel-axle, shafting, or pin on its bearing, all 

 the particles of the constrained body move in concentric paths. 



In the third mode of constraint each particle of the body has 

 a helical path, that is, each particle rotates about the same centre, 

 but this centre is itself being displaced in a straight line. That is, 

 the displacement of the whole body is composed of a translation 

 and a rotation. Any hollow screw forms a helical guide. 



It is important to note that it makes no difference in any 

 of the above examples which is at rest, the constraining or 

 the constrained body. This follows from what has been pre- 

 viously said about the relativity of motion. 



A little consideration will make clear the following state- 

 ments : 



1. That if one point in a body be fixed, there can only be 

 rotation taking place in that system, but the rotation may 

 take place in any direction. 



2. That if two points in a body be fixed, then the given 

 system is still capable of undergoing rotation, but the rotation 

 in question can only take place about the straight line in which 

 these points are found. This straight line is called the axis of 

 rotation. 



3. If three points which are not in the same straight line 

 be fixed, then there can be no movement of the body. 



4. If one point in a body be constrained to move parallel to a 

 line, the body may undergo rotation or translation or both. 



5. If two points in a body be constrained to move parallel to 

 a line, the body may be translated or rotated in one plane. 



6. If three points in a body be similarly constrained, the 

 body may only be translated. 



28. The Conversion of Circular into Rectilinear Motion, 

 We may readily show that a body may be constrained in two 

 directions at right angles to one another, so as to take a 

 circular path. The rectilinear motion of the bar (fig. 9) be- 

 tween the guides at c and D causes the block E, moving in the 

 groove A B, to have a circular path. The circular motion is 

 produced by two sliding constraints at right angles. 



The conversion of circular into rectilinear motion (or, as it 

 is called, reciprocating motion, on account of the to-and-fro 



