810 Parallel Motion of Sarrut and some Allied Mechanisms. 



with less than eight pieces of connexion and eight or more 

 hinges (some o£ them multiple) : or six pieces of connexion 

 and ten hinges. The simplest rectilinear point-movement 

 uses five moving pieces and seven hinges. 



§ 6. It may be not amiss to mention certain very familiar 

 objects in which the mechanisms here discussed are fore- 

 shadowed and, in a sense, are even potentially contained. 

 The bellows used in blowing organs * have, since about the 

 year 1419 f, been made with each of the four collapsible sides 

 or walls composed of two wooden plates (ribs so-called), 

 hinged together along the horizontal median line, as an 

 improvement on mere folds of leather. A horizontal lid and 

 base, hinged to the ribs, with suitable gussets of leather at 

 the eight corners, complete the apparatus. The step, which 

 took so long in making, from this mechanism to the parallel 

 motion of Sarrut, consisted in removing two of the adjacent 

 walls, and realizing that the rectilinear up-and-down motion 

 of the lid was then not only still a possible movement but 

 the only movement possible. (Removal of opposite walls 

 would of course at once leave the mechanism with two degrees 

 of freedom.) Again, too, in the folding flaps which connect 

 the edges of the two boards of some portfolios we may see, 

 in an approximate form, the details of the mechanism (a). 

 Some purses, pocket-books, and card-cases show the same 

 arrangement. In all such instances, however, the very crucial 

 and distinctive omission of the actual and principal hinge 

 remains to be made before the singular mechanism [a) is 

 realized. 



§ 7. Some of the foregoing explanations may appear need- 

 lessly explicit ; but the difficulties of picturing and describing 

 adequately mechanisms of a specifically three-dimensional 

 character (a large class too little studied so far) may be 

 sufficient excuse. Mistakes and misconceptions arise only 

 too easily in this region. Sarrut himself, for example, 

 appears to have thought that any closed chain of six pieces 

 would be normally free ; and Brunei, desiring to convert 

 his parallel piece-motion into a rectilinear point-motion, 

 figures and describes a spurious mechanism which is nothing 

 but a stiff framework. 



* Willis has the suggestion "organ-bellows'' written against his 

 sketch. 



t Grove's Dictionary of Music : Article " Bellows." 



