It is noted that a differential rotation 68 about an
arbitrary unit vector S is equivalent to three
differential rotations, 69x, 68y and 689, about the
X, Y and Z axes. Finally, the error movement of the
platform may be expressed as a vector as follow:
6GS S
H = 8 (5.43)
8dH So H x S
The range of uncertainty of the position of any point
in the end-effector body, say, the point H, is shown in
Fig. 5.7. Such uncertainty in space can be approximated by
a small parallelepiped, whose three edges are 6h, p68 and
6p. Here, 8h is the axial position error, p is the distance
of point H from the error screw axis $, 58 is the angular
error range and 6p is due to the uncertainty of position of
the screw axis.
5.7 Summary
The mechanical error analysis of a six degree-of-
freedom parallel manipulator has been studied in this
chapter. Matrix transformations, widely used in spatial
mechanisms, are applied. The screw theory, as applied to
determine the instantaneous kinematics of fully parallel
manipulators, is utilized. Numerical example is presented
to show how to determine the reciprocal screws in each
subchain. Velocities and small displacements of the joints