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a force is perpendicular to the direction of the prismatic
pair, there is no contribution by this force to the rate of
working. Also, an revolute pair perpendicular to the
direction of a couple also satisfies the condition of
reciprocity. All couples, no matter how they are oriented,
are reciprocal to a pure translation in a direction parallel
to a prismatic pair. Therefore, if a body is constrained to
move about an ISA (Instantaneous Screw Axis), c, a wrench
acting on a screw C' can contribute nothing to the rate at
which work is being done on the body. In such a
circumstance i and C' are said to be reciprocal screws.
The necessary and sufficient condition for a pair of
screws, 11 = S1 + eS,1 and $2 = a2 + eSo2, to be reciprocal
can thus be expressed as
$1 0 $2 = SI So2 + S2 Sol = 0 (5.16)
where the symbol o denotes the reciprocal product of a pair
of screws.
5.4 Screws of the Relative Motion of the Joints
In order to calculate the screws representing the
relative motion of the joints, we would like to have each
joint expressed with respect to the global system OXYZ.
Let jif(Sji, oji) denote the motion screws of the
joints with respect to the OXYZ system, where j = 1, 2,...,
6 denote the joints and i = 1, 2 and 3 denote the subchain.
Thus, representations of the screws are