上海交通大学：《复杂系统动力学计算机辅助分析》课程教学资源_Chapter 3_CHAP3.3-Relative Constraint

3.3 Constraint between pairs of bodies Relative angle constraint ·Revolute joint 。Translational joint Relative distance constraint

2022年3月11日 3.3 Constraint between pairs of bodies • Relative angle constraint • Revolute joint • Translational joint • Relative distance constraint

Relative angle constraint B B;is constrained to undergo translational motion without rotation relative to b B 01-p,=C3 def ro(i,j) =p,-p,-C3=0 g=ggy4,=(9,4,=69,0 x DOF=n-s=6-1=5 市9u,》=p,-p,=0 D,w=[00刂 Φ，》=[00-1 v'o,》=0 Parameter: i,C3 ro1》=0,-0,=0 ra(=0

Relative angle constraint Bi is constrained to undergo translational motion without rotation relative to Bj  j i  c3  0 def ( , )  r i j  3 c  j i  • Velocity constraint equation 0 ( , )     j i r i j     0 ( , )  j  i  r i j        3 Parameter: i, c j r Bj y  x  O j x  i y  Cj  j DOF  n  s  6 1  5   T T i i i q  r 0 0 1 ( , )  r i j j   q 0 a ( )   i  0 ( , )  r i j v    T T j j  j   q  r T T T q  qi qj 0 0 1 ( , )   r i j i   q i r i i x  i y  Bi  c

Revolute joint Definition B;is constrained to undergo rotational motion without translation relative to B, Revolute constraint

Revolute joint • Definition Bi is constrained to undergo rotational motion without translation relative to Bj Revolute constraint

Description of the constraint Inertial frame O-e Body-fixed frame of B C 4=p)' Pointo sosy) Body-fixed frame of B,C,- 4,-g,)r Point p 5s=(kPyP）y Point P and Q coincide 9-=0r9-r=07+s9-1-s=0 def 鸿=+9 D》=r+A,s9-r-As”=0 =+

• Description of the constraint Bj y  x  O j x  j y  Cj j r  Q Q j r Q j s e  Inertial frame O  C j j e  Body-fixed frame of Bj    T T j j  j q  r Point Q Q j s   Q T j Q j Q j s  x  y  Point P and Q coincide def ( , )  r i j Φ P i s   T T i i i q  r Point P P i s   T P i P i P i s  x  y  i x  i y  Ci P ir Q j j Q j r r s      P i i P ir r s      0      P i Q j r r P i i i Q j j j r  A s  r  A s  0 Bi i r   0 P i Q j r r     0 P i i Q j j r s r s Ci i e  Body-fixed frame of Bi  P

DuW=了+A,s9-1-AsP=0 Number of constraint s=2 4,=9,'9,=(9) q=gg)'=(9,yp, Degrees of freedom δ=n-S=4 n=6 Parameters of the constraint i,,s=y）,s9=(x9) Φ》= 。agg儿-

    T T , , , Q j Q j Q j P i P i P i i j s  x  y  s  x  y  s  2 Degrees of freedom   n  s  4 Number of constraint   T T j j  j q  r Parameters of the constraint        0 P i i i Q j j j r i j Φ r A s r As ( , )   T T i i i q  r     T T T T T T i j i i j  j q  q q  r r  0                                              P i P i i i i i i i Q j Q j j j j j j j r i j y x y x y x y x          sin cos cos sin sin cos cos sin ( , ) n  6 Bj y  x  O j x  j y  Cj j r  Q Q j r Q j s P i s i x  i y  Ci P ir Bi i r P