262 



NA TURE 



[July 11, 1S95 



Argeiiioiu, by Dr. D. Prain, a description of a new species of 

 Bryopsis, and of a peculiar mode of growth in another sj)ecies, 

 by Miss E. S. Barton ; an account of fossil plant-remains in 

 peat, by Mr. A. depp ; and a description of a lar^e number of 

 new species of (Jrchidac&v, by Mr. A. B. Kendle, from the 

 plants brought by Mr. Scott Elliot from Tropical Africa. 



SOCIETIES AND ACADEMIES. 

 London. 



Royal Society, May i6.— " The Complete System of the 

 I'eriodsofa Hollow Vortex Ring." By II. C. Pocklington. 



May 30. — "The Kinematics of Machines." By Prof. T. A. 

 llearson. 



In this paper it is shown that all machine movements, however 

 complex, are derived from the association together of some of a 

 comjiaratively limited number of kinds of simple motions, which 

 take place l)et»een consecutive directly connected ])ieces. 



Certain geometrical laws are enunciated, from which are 

 derived the conditions necessary for the assixiation of those 

 motions together in one machine. It is shown that those laws 

 preclude the existence of certain combinations of motions. By 

 attaching to each kind of motion a suggestive symbol a method 

 of expressing the constitution of a machine movement by a 

 simple formula is proposed, whereby similarities and differences 

 between machines may be exhibited at a glance. 



The author commences by considering a mechanism, consisting 

 of four bars united in one continuous linkage by four pins which 

 have (larallel axes. By imagining the length of the links lo 

 undergo variation from zero to infinity, it is shown that this 

 mechanism is representative of all the simple plane mechanisms, 

 and, by inuagining other variations lo occur, it is shown to be 

 representative of slill further classes of mechanisms, in which 

 the parts do not move in or |>arallel lo one plane. In this the 

 relative motions of consecutive pieces are either turning, when 

 one piece revolves completely around relatively to the other, the 

 reprcsenlative .symbol being the letter O, or swinging, when one 

 piece turns through a limited angle relatively to the adjoining 

 one, represented by the letter U. 



O Gttrip. 



Q Croup. 



O Croap. 



D Croup 



F^ n 



n 



•r-^' 



( 



■3 





By the application of the governing laws 14 distinct comliina- 

 tions are found to be possible, and only 14. They are exhibited 

 by the following formuhv, in which a large 1) associated witli a 

 small o signifies that in one case adjacent links turn relatively 

 to one another so as to continxiously increase the angle between 

 them, and in the other to continuously iliminish the angle. The 

 double ®) signifies that two complete re\olutions accompany one 

 complete to-andfro ssving or slide. 



Applying Reuleaux's principle of " Inversion " it will be seen 

 that 32, and only 32, distinct machine movements can be 

 derived from the above 14 mechanisms. Those from the same 

 mechanism are distinguished from one another in the fornnila 

 by using a thick line for the frame link. For example, 



/0~Ok signifies a machine movement like that employed in the 

 V^J j' crank-and-connecting-rod engine. 



The first law enunciated, which governs the association of the 

 O and U motions, is founded on the geometrical fact that the 

 sum of the four angles of the i|uadrilateral is constant. After a 

 complete revolution the angle between the bars is considered lo 

 have been increased or <liminished liy 2ir. 



From this it is impossible for only one motion lo be turning 

 and the other three swinging, otherwise the sum of the four 

 angles would increxsc or decrease by 2ir each revolution. 



The second law, which governs the association of the motions, 

 has lo do with the proixirtions between the length of the links 

 neceswry to |)ennit of complete turning. This is founded on 

 the fact that one side of a triangle cannot lie greater than the 

 sum of the other iwo. From these two laws together it is 

 shown that it is impossible to have Iwo <Js alternating with 

 two L's. 



Next it i.s jx)inted out how the U motion may be provided for 

 by conMrucling a circular slotway in one piece, and shaping the 

 other piece to lit the slotway, so that by imagining the radius of 

 curvature of ihe -ilotwny to be iniiefmilely increased a relative 

 ""■'*' ■ sliding motion, represented by the 



*)'"' ubslituted for the swinging motion 



'-'••■■ '1 to \k a swing through a zero angle 



aUiut an I'nire, the previously mcniioneil laws 



will appl) >iilaining I motions, anil It will follow 



that a coinbiiuitiun o( three slides and one swing is precluded 

 by ihc firM law. 



NO. 1341, VOL. 52] 



O 



,0-cn 



is exemplified in the oscillating engine nnich used in 

 liaddle-wheel steamers. 



(_^ jl is found in Slannah's pendulum pump, and 



/tr"CN ijuadrupled is the movement ado|>ted by Kigg in the 



The author next discusses the relation of cams and spur-w heel 

 mechanisms to the foregoing kinematic chains, showing that 

 they are the result of the suiijiression of one of the previous four 

 links and the amalganiation of the two adjoining simple motions 

 into one more complex. A comparison is also made with belt 

 gearing, and expressive formuhe suggested. 



The author then passes to the consiileration of machines the 

 parts of which do not move jxtrallel li> one plane. 



The first 13 of the previously mentione<l mechanisms have 

 their counter|>art in mechanisms the jiarts of which ntove 

 (xirallei lo the surface of a sphere, llooke's joint is the best 

 known example. The 14th consisting of 3 slides cannot be 

 adapted to a sphere but it can to a cylinder, and iVom it are 

 <lerived 4 possible screw mechanisms. 



The remaining mechanisms consist of those in which the axes 

 of the turning and swinging motions neither meet nor are 

 parallel. They include the motion which oecms at a ball-ami 

 socket joint. The method of classification according to the 

 proposed scheme is simimarised as follows: — 



All simple machine movements may be ranged in four divisions, 

 viz. : — 



(i) Consisting of plane mechanisms. In which the pieces move 

 in or |)arallel to the surface of a plane. 



(2) Spherical mechanisms. In which the pieces move In or 

 parallel to the surface of a sphere. 



(3) Cylindrical mechanisms, in which ihe pieces nuive in or 

 ])arallel to the surface of a cylinder. 



(4) The remainder, to which the name conoidical mechanisms 

 is given, in which the axes of ihe swinging and turning nioiions 

 neither meet nor are parallel. 



The mechanisms in each of these divisions are classed in two 

 subdivisions. 



Subdivisi(m .S, with .surface contact of consecutive linU^. 



Subdivision P, with point contact of consecutive links. 



The mechanisms In each of the eight subdivisions are still 

 further subdlvideil into combinations. The comliinatiims of In 

 2,, and 3,, are exh.austlvely enumerated, and it is suggested that 

 an extension of Ihe methods of applying the geometrical laws 

 would lead to the preparation of an exhaustive list ol the 

 possible combinations In (he other subdivisions. The coniliina- 

 tions are still further subdivided Into Inversions according to 

 Reuleaux's principle of the Inversion of a machine. 



Lastly, the author proceeds to show how the foregoing con- 

 siderations .assist in Ihe analysis of compound mechanisms. Hi; 

 Is assumed th.at practically all compoimd mechanisms contain a j 

 continuous mechanism A, of not nu)re than four links, from , 

 which definiteness of relative motion of all the other links is 

 derive<l. .\ny Iwo links of .\ in their exact length, or longer or j 

 shorter, may be adopted lo form wilh two new links a second i| 

 mechanism H, and any Iwo of A or li, or one of A and one of 

 H, may be adopted lo form with Iwo slill further added links a | 

 third merhanism C, and so on. In this way a delinllcness of 

 relative motion of many links in a compound mechanism is 

 derived. The notation lends itself to a clear exhibilion of the 



