pairs are not at right angle (a 0 90). The equation of
this form of torus can be expressed as
z2
{(x2 y2 + z2) (a2 + b2))2 = 4a2(b2 __-
sin2a
(3.3)
The diametral plane cuts the torus in egg-shaped curves as
shown in Fig. 3.4(b). For different twist angles (300, 45
and 750) and dimensions of the links (a > b, a = b, and a <
b) with each specified twist angle, the shapes of the torus
are shown in Figs. 3.8 3.10, respectively. It is noticed
that the diametral sections of these tori are similar to
those of the common form when a > b and a = b, but flattened
and egg-shaped. But the tori in Figs. 3.8 3.10 do not
intersect themselves when a < b, which differs from the
schematic shown in Fig. 3.6(c).
Symmetrical-offset form. The symmetrical-offset form
has the axes of the two revolute pairs at right angle (a =
900) and with offset (s # 0). The equation of this form of
torus can be expressed as
((x2 + y2 + z2) (a2 + b2 + s2)}2 = 4a2(b2 z2)
(3.4)
The diametral section of this kind of torus is shown in Fig.
3.4(c). For a > b and small s, the shape of the torus as
shown in Fig. 3.11(a) is slightly different from that in
Fig. 3.6(a). As shown in Fig. 3.11(b), the inner walls of
the anchor-ring become flatter when a = b. The two closed