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XXVIII. — A New Graphic Analysis of the Kinematics of Mechanisms. By- 

 Professor Eobert H. Smith, Mason College, Birmingham. (Plate 

 LXXXII.) 



(Read 19th January 1885.) 



A mechanism may be defined as a combination of plates, bars, or flexible 

 members jointed together, so that, while the parts may move relatively to each 

 other, the relative positions of all the different parts are determinate for each 

 given possible relative position of any two parts. 



It follows immediately that the simultaneous relative displacements, 

 velocities, and accelerations of velocity of all parts are also strictly determinate. 



This determination, by accurate graphic means, forms the subject of this 

 paper. In it those mechanisms alone are considered that are composed of 

 rigid members, the motions of whose parts are all continually parallel to one 

 plane, the constancy of the plane being defined relatively to one of the members 

 of the mechanism itself. 



The different rigid members of mechanisms will be termed "bars." That 

 bar relatively to which the displacements, velocities, and velocity-accelerations 

 are measured, will be termed the base-plate or bed-plate. The displacement, 

 velocity, and velocity-acceleration of the base-plate remain, of course, always 

 zero. 



To avoid repetition of the cumbersome phrase " relatively to," this phrase is 

 discarded for the shorter expressions "through," "past," "over," or "round." 

 Every possible motion or other vector is through some field in which positions 

 and directions may be defined in a determinate manner. It is improper to 

 speak of the motion of one point past another, without mention of the parti- 

 cular field through which the motion is measured, because two points alone are 

 inadequate to define a field in which vectors may be measured. In what follows, 

 when the field of reference is not mentioned, it is to be understood that the 

 vectors are taken through the "field of the base-plate," i.e., through the space 

 surrounding and defined with reference to the base-plate. On the other hand, 

 it is perfectly definite to speak of the motion of a point or of a bar over, past, 

 or round another bar, the motion being understood, without further mention, to 

 be measured through the field of the bar round which it takes place. 



The graphic determination of the simultaneous positions of the various bars 

 of most commonly used mechanisms is easy and well understood. When 

 difficulties occur, as in various engine reversing link-motions, the special 

 methods here explained enable them to be readily overcome. The loci of the 

 successive positions of the various parts maybe called the "motion curves" or 



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