PROFESSOR T. A. HE ARSON ON THE KINEMATICS OF MACHINES. 
23 
surfaces of mutual contact and means of constraint against other motions will be 
found to exercise a judgment which is required to be extensively informed, the variety 
of possible forms and means being often so great. What Reuleaux describes under 
the headings “ Complete and Incomplete Closure,” “ Force Closure,” “ Inversion of 
the Pair,” “Chamber Pair,” &c., will be found of great value in machine design ; but, 
in the first study of the kinematics of machines in general, it will be found advan¬ 
tageous to avoid the consideration of these details, and to study the conditions 
necessary to permit of the contemplated motions, without being concerned with what 
is necessary to preclude other motions. 
The great featui’e of Reuleaux’s theory is the enunciation, for the first time, of 
the principle known as “'the inversion of a mechanism.” By the aid of this, the 
family relationship between machines, which previously were thought to have little 
or nothing in common, is most clearly established ; and all the knowledge which has 
been acquired relative to one becomes applicable to the consideration of the others. 
The belief that the method of analysis here proposed is adapted to more perfectly 
and consistently express the effects of inversion, has been one of the chief encourage¬ 
ments to the author, in hoping that the adoption of his proposals will be advantageous. 
It may be stated that the object aimed at in the design of a machine is to obtain a 
special kind of movement of one or more pieces, of which the machine is composed, 
relatively to one’s self as a fixed observer or user of the machine. 
Any one of the four links (if there are four) may be fixed relatively to the user— 
may be made, as it is called, the frame link , about which all the other pieces move ; 
and we shall, in general, obtain a different kind of movement of those links with each 
change of the fixed link, the difference being such as to constitute practically a new 
machine movement, and yet all the four will be intimately related to each other, for 
they all have the same relative motions of the pieces composing them. 
This idea of the change of the fixed or frame link is what is called “ the inversion 
of a mechanism.” 
In order to assist in the description of the effect of inversion in causing a change in 
the machine movement, it will be convenient to adopt the term primary piece, 
originally proposed by Rankine, for those pieces or links which are in sequence with 
the frame link and move in contact with it. (Rankine must have been very near 
the discovery of the principle of inversion.) 
If we invert any one of the previously mentioned mechanisms, and, by making 
some other link the frame link, find one or both of the new primary pieces to have a 
different motion to that which the previous primary pieces had, a new machine 
movement will have been derived ; but if, as often happens, we find after inversion 
that both primary pieces move just like the previous primary pieces, no new 7 move¬ 
ment will result, but only a repetition of a previous one. Thus there are not 
necessarily four different machine movements derivable by inversion from every four- 
linked mechanism. 
