PROFESSOR T. A. HE ARSON ON THE KINEMATICS OF MACHINES. 
37 
through a joint, and in the formula may be represented, coupled to three other links, 
thus ~U—^— : U- , in which case the formula for the whole mechanism may be 
shown so 
U—I£- 
A—u— u - ■ y— u—4- 
-u 
The author has been unable to discover any actual machine in which determinate 
motion has been derived from such a method of accumulation of partial constraints. 
Passing to the compound mechanisms previously referred to, four degrees of com¬ 
plexity in the conjunction of two interdependent simple mechanisms may be specified. 
Conjunction I, when two adjacent links, T and V for example, of a mechanism A 
are adopted, in their exact length, to form with two new links, X a and Z a , the second 
mechanism B. In this case the new link X 3 is attached to V at the same joint, w, at 
which Xj is coupled, and Z 2 as well as Z l are united to T at the joint s. In this we 
have a third mechanism, B', consisting of the four links, X ] Z 1 Z. 2 X. 2 , united at the joints 
y x sy 2 w. Supposing U motions at all the joints, the formula for a compound mechanism 
so conjoined may be written thus, IT—IT—U—II—U. An example of this will be 
found in what is called a double Kite mechanism (see p. 25) consisting of four equal 
links forming a parallelogram, and two links longer but equal to one another, joined 
together at one end, and at the other ends united to two opposite corners of the 
parallelogram. Such a construction forms a part of the mechanism of Peaucellier’s 
straight-line motion. If the additional links of Peaucellier’s mechanism are omitted, 
it will be possible, with each Kite, to have the movement UOo 2 0 as before explained 
(p. 1 9). Now, if three links unite at a joint and each of two of them have an O motion 
relatively to the other then, relatively to one another, the motion must be either U or 
Oh A new symbol is therefore wanted to stand for a motion which may be either 
O, U, or O 3 , which it is, to be determined by tli6 context. The letter Q suggests 
itself, and accordingly the formula for the double Kite would be 
H—Q 1 —O'—Q—o 2 
All the previously-mentioned conditions as to the associations of the OUI motions 
in one chain, and the proportions of links requisite for any combination, will hold 
good of mechanism B, as well as A. Thus the letter Q in the mechanism above 
stands for 0 in each Kite mechanism, and for O 3 in the parallelogram mechanism. 
It will frequently happen that whilst the proportions of A will permit of O motions 
