{(x2 + y2 + z2) (a2 + b2 + s2)}2
z scosa
= 4a2{b2 ()2} (3.1)3
sina
Common form. The common form of torus (right
circular), sometimes called the anchor-ring, is shown in
diametral section in Fig. 3.4(a). The axes of the two
revolute pairs are at right angle (a = 900). Their common
perpendicular is a and the offset between them is zero (s =
0) (see Fig. 3.3). The equation of the torus can be
expressed as
{(x2 + y2 + z2) (a2 + b2)}2 = 4a2(b2 z2) (3.2)
The difference between the lengths of the links affects the
shape of the torus, which is illustrated in Fig. 3.6. As a
> b shown in Fig. 3.6(a), the two circles in the diametral
section are separated by a distance of 2(a b). This kind
of torus is also shown in Fig. 3.7. When the two circles in
the diametral section are tangent at a point, the origin 0,
then a = b as shown in Fig. 3.6(b). The torus will
intersect itself when a < b as shown in Fig. 3.6(c). There
is a void in this kind of torus when a < b exists.
Flattened form. The flattened form of torus has no
offset (s = 0) either, but the axes of the two revolute
3 The equation of the general form of torus is derived
in Appendix B.