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_CHAP3.2-Absolute constraints

3.2.Constraints between a body and ground (Absolute constraints) Absolute x constraint Absolute y constraint Absolute angle constraint Absolute distance constraint

• Absolute x constraint • Absolute y constraint • Absolute angle constraint • Absolute distance constraint 3.2. Constraints between a body and ground (Absolute constraints)

Absolute position constraint .Absolute x(y)constraint Point P of the rigid body B is constrained to move along the axis parallel to axis x or axis y of the inertial frame Absolute x constraint Absolute y constraint

Absolute position constraint • Absolute x(y) constraint – Point P of the rigid body Ba is constrained to move along the axis parallel to axis x or axis y of the inertial frame Absolute x constraint Absolute y constraint

Absolute x constraint B, Inertial frame O-e Body-fixed frame C,-e ,=(9,'sP=x”P Since=C =元+.匠+）-c=0 C x def x6+4s）-G=0x=[0] S=1 DOF=n-S=3-1=2 pax()=x,+x cosp-y sinpi-c=0 Parameters: i,sP=(xy）,c

• Absolute x constraint Bi y  x  O i x  i y  Ci i r i P P ir  P i s  1 c e  Inertial frame O  Ci i e  Body-fixed frame    T T i i i q  r   T P i P i P i s  x  y  1 x r c P  i    P i i P ir r s      def ( )  ax i    0 x  r  s  c1  P i i      0 1 T    c  P i i i x r A s cos sin 0 1 ( )  x  x   y  i  c  P i i P i i ax i    Since Parameters:   1 T i, x y , c P i P i P i s      T x  1 0 s 1 DOF  n  s  31 2

Φ)=xTG+AsP）-c=0 B 本0=xr(+AsP）=0 y Velocity constraint equation 市o=xr(G+RAsf0,)=0 市w=西，meg,-vaw=0,g,=上，J →Dm=erx'r4g]va0=0 Acceleration constraint equation Cx X p)=x"(+RAs",+RAs)=O A=RAO 本0=xT+RAs,-As2)=0 RR=-1 市m0=Φ，0i,-y0=0,4= →ym0=xAs02

• Velocity constraint equation   1 0 ( ) T      c  P i i i ax i x r As   0 ( ) T     P i i i ax i x r A s      0 ( ) T    i  P i i i ax i     x r RA s i ii  ( )  T        0 A  RA i P i i i P i i i ax i        x r RA s RA s RR  I   0 ( ) T 2      i  P i i i P i i i ax i      x r RA s A s • Acceleration constraint equation   T i T i i ax i i ax i ax i v i       q q r  q   0,  ( ) ( ) ( )    P i i ax i i x x RA s q   ( ) T T    T i T i i ax i i ax i ax i i        q q r  q   0,  ( ) ( ) ( )  ( ) T 2 i P i i ax i   x A s  Bi y  x  O i x  i y  Ci i r i P P ir  P i s  x c 0 ( )  ax i v

Absolute y constraint Inertial frame o-e B Body-fixed frame C-e C2 sP=(PP）J Since =元+5”，(+5）-02=00 X B0)=y+A,s;")-c2=0 y=[0 1 pardi)=y,+x sin +y cosp-c2=0 Parameters:,s=c

Bi y  x  O i x  i y  Ci i r i P P ir  P i s  2 c • Absolute y constraint e  Inertial frame O  Ci i e  Body-fixed frame    T T i i i q  r   T P i P i P i s  x  y  P i i P ir r s      def ( )  ay i    0 y  r  s  c2  P i i      0 2 T    c  P i i i y r A s sin cos 0 2 ( )  y  x   y  i  c  P i i P i i ay i    Since   T y  0 1 Parameters:   2 T i, x y , c P i P i P i s   