24 
PROFESSOR T. A. HEARSON ON THE KINEMATICS OF MACHINES. 
The link which is selected for the frame may be represented as follows :—If 
the links and motions are shown in circuit the frame link may be shown by a 
thickened line, thus, 
or if printed in line, thus —O 3 —o—I — o—, or thus. 
I j . Or, if the links themselves are left to the imagination, the link 
which unites the end letters of the line, may be understood to be the frame link, # so 
that 0 2 oIo means the same thing as either of the above three formulae, and IoO'~o is 
an inversion which ogives a new machine movement. 
oloO' 2 and o0 2 oI are inversions which give repetitions only of the previous 
movements. 
An exhaustive list follows of all the possible different machine movements which 
can be derived by inversion from the combinations of the OUI motions previously 
enumerated. 
They are divided first into four groups. These are sub-divided into fourteen 
combinations, and the fourteen combinations are still further divided into thirty- 
two so-called “inversions.” 
When four different movements are derivable from a combination, each of the four 
may be regarded as an inversion of either of the others, and it will not be inappro¬ 
priate in this case to say there are four inversions, or when only three or two different 
movements are obtainable, to say there are three or two inversions, respectively. 
When only one movement can be obtained it will still be desirable to speak of it as 
one inversion. 
* The author is indebted to one of the Referees, to whom this paper was submitted, for this sugges¬ 
tion and for some others. 
