Sarrut and some Allied Mechanisms, 807 



be regarded as composed of two spherical* mechanisms, each 

 of four pieces, placed in tandem with different centres. One 

 consists of a closed chain of four pieces ARSB con- 

 secutively hinged along four lines concurrent in X ; the other 

 similarly of four pieces ATUB with hinges concurrent in Y; 

 the pieces AB and also their hinge-line XY being common 

 to the two mechanisms. But the singular six-piece mechanism 

 described above arises only after the removal or omission of 

 the hinge XY, which is superfluous or redundant. The line 

 XY is then no longer an actual and mechanical hinge, but 

 yet remains kinematically as a virtual hinge-line, in respect 

 of the relative movement of A and B. 



This type of mechanism shall be referred to as (a). 



§ 4. From the type (a) two special forms are derivable by 

 taking one or both of the points XY at infinity. If one only, 

 say Y, is at infinity, a case (b) is obtained. The three 

 hinges connecting ARSB meet still in a finite point X ; but 

 the three hinges connecting ATUB are parallel ; and the 

 motion of A relative to B is a movement of pure rotation 

 about a virtual hinge-line parallel to the hinges last named 

 and passing through X (figs. 7, 8). This mechanism maybe 

 regarded as composed of a plane mechanism and a spherical 

 mechanism in tandem, with the common hinge of the two 

 common pieces omitted. 



If both X and Y are at infinity a case (c) arises. Each 

 set of three hinges forms a parallel system ; the movement 

 of A relative to B is a rotation about the line at infinity 

 which meets all the hinges, a rectilinear motion therefore in 

 the direction perpendicular to all the hinges. It is the type 

 of mechanism described by Sarrut. It may be regarded as 

 composed of two plane mechanisms in tandem ; these 

 mechanisms having parallel sets of hinges in two different 

 directions and having the virtual common hinge of the two 

 common pieces at infinity. In technical terms the two 

 mechanisms would be called crossed slider-crank chains, 



* The term is perhaps not well enough established to pass without 

 explanation. Mechanisms composed of pieces connected by hinges 

 which are all parallel, being sufficiently represented by any plane section 

 perpendicular to the hinges, are loosely and commonly spoken of as 

 %t plane " mechanisms. And by analogy mechanism^ of which all the 

 hinge-lines are concurrent in one point, being sufficiently represented by 

 ction in which they are cut by any sphere centred at that point, 

 may be called "spherical mechanisms. Custom, however, is variable, 

 lieuleaux uses the terms " cylindric " and "conic"; the relative motion 

 of any two pieces being representable by the rolling of cylinder on 

 cylinder in the one case and cone uuon cone in the other. 



