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Two-Dimensional Joint Constraints – Haug Notation
General
0
0
(^) q q (^) t 0
(^) q q (^) t
0
q q q 2 q (^) tt 0 q q q qt
(^) tt q q q q t q q q 2 q
Revolute
(^2) x 1
P i
P REV r (^) j r 0
P qi (^) REV I 2 Bi si '
P qj (^) REV I 2 Bj sj '
REV (^0 2) x 1
P i i
2 i
P j j
2 (^) REV j A s ' A s '
Double revolute
P i
P ij j
P i
P ij j
2 ij
T REV_REV ij
for d r r and d r r
d d C 0
^
qi REV
T qi (^) REV_REV 2 dij
qj REV
T qj (^) REV_REV 2 dij
REV _REV 0
(^) ij
T REV ij
T REV _REV^2 dij^2 d d
Parallel vectors
^ ^ ^
P j
Q j j
P i
Q i i
j
T T PARALLEL i
for a r r and a r r
a R a 0
j
T qi (^) PARALLEL (^01) x 2 ai a
j
T qj (^) PARALLEL (^0 1) x 2 ai a
PARALLEL 0
PARALLEL 0
Pin-in-slot
P i
P ij j
P i
Q i i
P i
P ij j
ij
T T PIN_SLOT i
for d r r and a r r and d r r
a R d 0
^ ^
ij
T qiREV 1 x 2 i
T T qi (^) PIN_SLOT a (^) i R 0 a d
qjREV
T T qj (^) PIN_SLOT a (^) i R
PIN _SLOT 0
ij REV
2 i
T i ij
T (^) PIN _SLOT a (^) i 2 d R d
Relative angle
ANGLE jiOFFSET 0
qi (^) ANGLE
ji (^) ANGLE
ANGLE 0
ANGLE 0
Acceleration Right-hand Side for Revolute
(^) tt q (^) q q t q q 2 q
(^2) x 1
P i
P REV r (^) j r 0
i
i i i
i i
r q
r q
P qi (^) REV I 2 Bi si '
P i i i i i
P i qi i 2 i i r B s '
r q I B s '
(^) i (^) i (^) i
P (^) qi q (^) i qi (^02) x 2 iAi si ' B A
^
P i i
2 i i
P i qi i qi i 2 x 2 i i i A s '
r q q 0 A s '
P qi (^) REV I 2 Bi si '
(^) j (^2) x 1 qi (^) t 2 x 3 qit 0 q 0
(^) t (^0 2) x 1 (^) tt (^0 2) x 1
(^) tt q (^) q q t q q 2 q
A s ' forbodyi
P i i
2 (^) REV i
A s '^ forbodyj
P j j
2 (^) REV j
^
P i i
2 i
P j j
2 (^) REV j A s ' A s '
