surface of a torus. The subworkspace of each open subchain
is the volume swept by this torus translated along the axis
of each ground-mounted (R-L) joint. In this chapter, the
shapes of the above-described torus of the subchain are
studied for different dimensions of the links. The
conditions on the dimensions of the links, for which the
subworkspace has no hole, are presented. Of course, an
infinitesimally small platform is not practical, because the
three spherical pairs supporting the platform coincide.
Therefore the platform has no controllability of its
orientation. To have controlled orientation, the platform
requires three controllable rotational degrees of freedom
with concurrent non-coplanar axes. This is attained by
placing the three spherical joints at finite distances from
one another. Nevertheless, the workspace study with
infinitesimally small platform is a useful step toward more
practical workspace studies with finite-size platforms
having controllable orientation, which will be covered in
Chapter 4.
One basic need in the design of mechanical manipulators
is to determine the shape of the workspace. Workspace
analysis of mechanical manipulators has been investigated by
many authors. Almost all the studies are related to
open-loop multi-degree-of-freedom serial-link mechanical
manipulators. Little work has been done in the area of
mechanical manipulators with parallel kinematic chains.