OBSERVATIONS OF CHANGE OF POSITION 31 



7. Show that if two adjacent sides of a parallelogram represent in 

 direction and magnitude the displacements produced in equal intervals 

 of time by two given causes, then the diagonal line between them must 

 represent the direction and magnitude of the displacement produced in 

 the same interval of time when these causes act simultaneously. 



8. Show that the statements which have been made about displace- 

 ments which take place in equal intervals of time must necessarily 

 apply to speeds. 



9. Show by diagram how to find resultant of any number of dis- 

 placements occurring simultaneously in the same plane. 



10. Construct a wire model to exhibit the resultant of several dis- 

 placements in different planes. 



27. Examples of Mechanical Constraint of Motion. The 



ordinary methods of constraining motion or rendering- 

 it determinate, and those which may be seen illustrated 

 very frequently in machinery, are three in number, viz., the use 

 of (1) guiding grooves or slots to allow sliding only, (2) pin and 

 eye to allow turning only, (3) helix or screw guides, to allow 

 screwing only. It will be seen that grooves and slots only 

 allow translation in the direction of the groove. The pin and 

 eye allow only rotation about an axis, while the helix allows 

 rotation to proceed simultaneously with translation. It will 

 be seen that the rigidity of solid matter is here utilised to 

 prevent movement except in the desired directions. 



These modes of constraint really form the basis of machinery. 

 We may obtain from them examples of all the kinds of dis- 

 placement of which a body has been shown to be capable. 

 But inasmuch as a body near the surface of the earth has always 

 a tendency to move towards the earth, we always find the 

 other movements of a body modified by this tendency, which 

 also largely influences the structure of machines themselves. 



The most common as well as the most effective mode of con- 

 straint is that in which a body moves along a straight groove ; 

 examples of this may be seen in a piston working in a cylinder, 

 and guide-blocks working in their guides. A lathe-bed or 

 optical bench will also serve as examples. In these cases it 

 will be seen that all particles of the guided and constrained 

 body have parallel rectilinear paths. 



In cases of the second mode of constraint, such as the 



