CHAPTER 4
THE WORKSPACE OF THE MANIPULATOR WITH FINITE SIZE PLATFORM
4.1 Introduction
This chapter deals with the workspace determined by the
geometric method which was developed in Chapter 3 as well as
the consideration of finite size platform of the
manipulator. The lengths from the center of the platform,
H, to the centers of the spherical joints, C1, C2 and C3,
affect the volume of the workspace, and more significantly,
the rotatability of the platform about the center H. Thus,
to get a workspace of the manipulator with rotatability of
the end effector as large as possible, the lengths between H
and Ci (i = 1, 2, 3) should be as small as possible,
consistent with controllability of end-effector orientation.
When, in the limit, the lengths are infinitesimal or zero,
we get the largest theoretical workspace with complete, but
uncontrollable rotatability of the platform.
The workspace of the parallel manipulator is defined
here as the region within which every point can be reached
by the center of the platform, H, of the manipulator (Fig.
3.19). The volume of the workspace is correlated with the
orientation and the rotatability of the platform, because it
is often important for a designer to know the rotatability
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