Similarly, the reciprocal screws r$1i and r$2i,
reciprocal to all other screws in subchain i (i = 2 and 3)
but li and $2i, respectively, can be found as the positions
and orientations of joint Ci are given and therefore are not
listed here.
It is noted that a force dose not affect the rotation
around a revolute joint when its line of action is parallel
to or along the axis of revolute joint. This is also the
reciprocity condition.
5.5 Jacobian Matrix
Let w$ represent the motion screw of the platform with
respect to the global system OXYZ, which can be expressed as
6 3
u$ = E E wjilji (5.23)
j=1 i=1
Taking reciprocal products with reciprocal screws r11i and
r$2i of Eq. (5.23) respectively yields
"$ O r$1i = 1liili 0 r$li (5.24)
and
$ o r$2i = W2i22i 0 r$2i (5.25)
where the symbol o denotes the reciprocal product of a pair
of screws and i = 1, 2 and 3. Thus, we can obtain the
following equation: