14 



THE HUMAN MOTOR 



along the straight line XX', any point M in the circumference 

 of that circle traces out a curve ABD, which is called a cycloid. 

 Any point on the wheel ot a vehicle running on a level surface 

 describes this curve. 



The line X X' on which O rolls is called the base. 



* A R C Cycloid D 



FJO. 22, 



The curve is repeated after the circle has made a complete 

 revolution as show r n at A and D, 



If, instead of the base being a straight line, it is itself the cir- 

 ference of a circle, two 

 other varieties of the 

 cycloid are produced. 

 These are called the 

 Epicycloid or the Hy- 

 pocycloid according as 

 the generating circle O 

 rolls outside or inside the 

 base circle. These two 

 curves are shown in figs. 

 23 and 24 respectively. 



It is to be noted also that in a cycloid the position of the 

 point M is given by the tangent of the curve at that point, MT ; 

 the normal MR of that tangent will cut the diameter RR', 

 pendicular to the base, at a point R, which is the point of contact, 

 between the circle and the base. In short, the different positions 

 of M might be considered as the result of the rotations round the 

 points R 1( R 2 . . . thus determined, these points being called 

 instantaneous centres of rotation (fig. 25). 



Epicycfoid 

 FIO ->3 



Hypocycloid 



Fio. 24. 



R R, 

 FIG. 25. 



Generally speaking, every figure moving in its plane can pass 

 from a position ( 1 ) to a position (2) by means of a rotation rouncl 



