Thus we are free to substitute the negative reaction force for any action force at any
joint. This has been done on link 3 in the figure in order to reduce the unknown forces at
that joint to one, namely F 32. The same procedure is followed at each joint with one of
the action-reaction forces arbitrarily chosen to be solved for and its negative reaction applied
to the mating link.
The naming convention used for the position vectors (Rap) which locate the pin
joints with respect to the CG in the link's nonrotating local coordinate system is as follows.
The first subscript (a) denotes the adjoining link to which the position vector
points. The second subscript ( p) denotes the parent link to which the position vector
belongs. Thus in the case oflink 2 in Figure 11-2b, vector R 12 locates the attachment
point of link 1 to link 2, and R32 the attachment point of link 3 to link 2. Note that in
some cases these subscripts will match those of the pin forces shown acting at those
points, but where the negative reaction force has been substituted as described above, the
subscript order of the force and its position vector will not agree. This can lead to confusion
and must be carefully watched for typographical errors when setting up the problem.
Any external forces acting on the links are located in similar fashion with a position
vector to a point on the line of application of the force. This point is given the same letter
subscript as that of the external force. Link 3 in the figure shows such an external
force F p acting on it at point P. The position vector Rp locates that point with respect to
the CG. It is important to note that the CG of each link is consistently taken as the point
of reference for all forces acting on that link. Left to its own devices, an unconstrained
body in complex motion will spin about its own CG; thus we analyze its linear acceleration
at that point and apply the angular acceleration about the CG as a center.