26.] 



PLANE MOTION. 



the whole motion can be produced by the rolling of a circle of 

 radius a within a circle of radius 2 a. 



The student is advised to carefully carry out the construc- 

 tions indicated in this as well as the following problems. Thus, 

 in the present case, draw the moving figure, i.e. the line AB, 

 in a number of its successive positions in each of the four 

 quadrants, and construct the instantaneous centre C in every 

 case. This gives a number of points of the space centrode. 

 Then take any one position of AB and transfer to it as base 

 all the triangles ABC previously constructed. The vertices 

 of these triangles all lie on the body centrode. 



26. To find the equation of the path of any point P of the 

 moving figure, let this 

 point be referred to a co- 

 ordinate system fixed in, 

 and moving with, the fig- 

 ure (Fig. 7) ; let the mid- 

 dle point O r of AB be 

 the origin, and O'A the 

 .axis O'x', of this system. 

 Then the co-ordinates x', 



Fi 



j/ f of P in this moving 



system are connected with 



its co-ordinates x, y in the fixed system Ox, Oy by the following 



equations, 



' cos<, 



y(ax ! ] 



where < is the angle OAB that determines the instantaneous 

 position of AB. Solving these equations for sin< and cos0, 

 squaring and adding, we find for the equation of the path of P 



_ 



- 



Or ^~ 



