Table A.1 Direction cosines spatial heptagon (set 1)
Ji(0 0
S2(0 -s12
S3(X2 Y2
s4(X32 Y32 ,
5(X432 432 Y32
6(X5432 Y5432
S7(X65432, Y65432,
1 )
c12
z2 )
Z32
Z432
Z5432
265432)
12(1
a23(c2
a34 (32
a45(w432
a56(W5432
a67(W65432
a71(c1
, 0
'U21
-U321
-U4321
-U54321
S-U654321'
, -si
0
U21
U321
U4321
U54321
U654321)
0
Therefore, the coordinates of joint C with respect to the
local coordinate system can be expressed as follows:
Cx = al2c1 + S22s12S1 + a23(C1c2 S1S2C12)
Cy = al2s1 S22s12c1 + a23(s1c2 + c1s2cl2)
C, = Sl + S22c12 + a23s2s12
(A.3)
(A.4)
(A.5)
The above expression are the same as those in Eq. (2.5)
except for different notation for elements of the subchain.
A.2 Subchain (R-L)-P-S
As shown in Fig. A.2, the coordinates
respect to the local coordinate system can
similarly as
of joint C with
be obtained