equations of the boundaries of the subworkspace, which is
the volume swept by this torus as the R-L joint translates,
will be derived.
3.3.1 Shapes of the subworksoace
Fichter and Hunt [51] have geometrically described and
analyzed four forms of the torus, which are common,
flattened, symmetrical-offset and general forms as shown in
Fig. 3.4. They also introduced two types of bitangent-
plane2, A-type, whose quartic curve intersection with the
torus always encircles the OZ axis and B-type, whose points
of tangency are both on one side of the OZ axis. Any
bitangent-plane to any form of torus cuts the torus in two
circles of the same radius which intersect one another at
the two points of tangency. The curve of intersection of
the bitangent-plane and the torus can be obtained by the
simultaneous solution of the equations of the bitangent-
plane and the torus. The curve of intersection of A-type
bitangent-plane and a common torus (a > b) is shown in Fig.
3.5.
The equation of the surface of a completely general
form of torus can be expressed as follow:
2 A bitangent-plane has two points of tangency with a
toroidal surface.