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Reference: Chapter 2 in Multibody Mechanics and Visualization by Harry Dankowicz, published by Springer Verlag UK, 2004.
To illustrate the use of auxiliary observers to represent linked mechanisms.
This Mambo project contains two non-stationary blocks and a non-stationary cylinder. The non-stationary blocks are constrained to coincide at one end with the non-stationary cylinder. The cylinder is fixed relative to one of the blocks. The linked mechanism may be positioned and oriented relative to the world observer in three independent steps, namely
l1, l2, and l3: lengths of the sides of the blocks.
radius: radius of the cylinder.
q1, q2, and q3: coordinates of the center of the cylinder in a coordinate system with origin at the reference point of the world observer and axes parallel to the basis vectors of the reference triad of the world observer.
q4, q5, and q6: 3-2-1 sequence of Euler angles representing the orientation of the first block relative to the reference triad of the world observer. theta: angle of the rotation of the second block about the joint. hinge.zip (zip file, 7 kb, December 30, 2012) 
>Restart():
>DeclareObservers(world,auxiliary_observer_A1,auxiliary_observer_A2,rod1,rod2): >DeclarePoints(W,Joint,Rod1,Rod2): >DeclareTriads(w,a1,a2): >DefineObservers([world,W,w],[auxiliary_observer_A1,Joint,a1],[auxiliary_observer_A2,Joint,a2],[rod1,Rod1,a1],[rod2,Rod2,a2]): >DefinePoints([W,Joint,w,q1,q2,q3],[Joint,Rod1,a1,l1/2,0,0],[Joint,Rod2,a2,-l1/2,0,0]): >DefineTriads([w,a1,[q4,3],[q5,1],[q6,3]],[a1,a2,theta,2]): >DefineNeighbors([world,auxiliary_observer_A1],[auxiliary_observer_A1,rod1],[auxiliary_observer_A1,auxiliary_observer_A2],[auxiliary_observer_A2,rod2]):
>DefineObjects( [rod1,'Block',point=MakeTranslations(a1,0,l2/2,l3/2),xlength=l1,ylength=(l1+l2+l3)/30,zlength=(l1+l2+l3)/30,color=yellow], [rod1,'Block',point=MakeTranslations(a1,0,l2/2,-l3/2),xlength=l1,ylength=(l1+l2+l3)/30,zlength=(l1+l2+l3)/30,color=yellow], [rod1,'Block',point=MakeTranslations(a1,0,-l2/2,-l3/2),xlength=l1,ylength=(l1+l2+l3)/30,zlength=(l1+l2+l3)/30,color=yellow], [rod1,'Block',point=MakeTranslations(a1,0,-l2/2,l3/2),xlength=l1,ylength=(l1+l2+l3)/30,zlength=(l1+l2+l3)/30,color=yellow], [rod1,'Block',point=MakeTranslations(a1,l1/2,0,l3/2),xlength=(l1+l2+l3)/30,ylength=l2,zlength=(l1+l2+l3)/30,color=yellow], [rod1,'Block',point=MakeTranslations(a1,l1/2,0,-l3/2),xlength=(l1+l2+l3)/30,ylength=l2,zlength=(l1+l2+l3)/30,color=yellow], [rod1,'Block',point=MakeTranslations(a1,-l1/2,0,-l3/2),xlength=(l1+l2+l3)/30,ylength=l2,zlength=(l1+l2+l3)/30,color=yellow], [rod1,'Block',point=MakeTranslations(a1,-l1/2,0,l3/2),xlength=(l1+l2+l3)/30,ylength=l2,zlength=(l1+l2+l3)/30,color=yellow], [rod1,'Block',point=MakeTranslations(a1,l1/2,l2/2,0),xlength=(l1+l2+l3)/30,ylength=(l1+l2+l3)/30,zlength=l3,color=yellow], [rod1,'Block',point=MakeTranslations(a1,l1/2,-l2/2,0),xlength=(l1+l2+l3)/30,ylength=(l1+l2+l3)/30,zlength=l3,color=yellow], [rod1,'Block',point=MakeTranslations(a1,-l1/2,-l2/2,0),xlength=(l1+l2+l3)/30,ylength=(l1+l2+l3)/30,zlength=l3,color=yellow], [rod1,'Block',point=MakeTranslations(a1,-l1/2,l2/2,0),xlength=(l1+l2+l3)/30,ylength=(l1+l2+l3)/30,zlength=l3,color=yellow]): >DefineObjects( [rod2,'Block',point=MakeTranslations(a2,0,l2/2,l3/2),xlength=l1,ylength=(l1+l2+l3)/30,zlength=(l1+l2+l3)/30,color=yellow], [rod2,'Block',point=MakeTranslations(a2,0,l2/2,-l3/2),xlength=l1,ylength=(l1+l2+l3)/30,zlength=(l1+l2+l3)/30,color=yellow], [rod2,'Block',point=MakeTranslations(a2,0,-l2/2,-l3/2),xlength=l1,ylength=(l1+l2+l3)/30,zlength=(l1+l2+l3)/30,color=yellow], [rod2,'Block',point=MakeTranslations(a2,0,-l2/2,l3/2),xlength=l1,ylength=(l1+l2+l3)/30,zlength=(l1+l2+l3)/30,color=yellow], [rod2,'Block',point=MakeTranslations(a2,l1/2,0,l3/2),xlength=(l1+l2+l3)/30,ylength=l2,zlength=(l1+l2+l3)/30,color=yellow], [rod2,'Block',point=MakeTranslations(a2,l1/2,0,-l3/2),xlength=(l1+l2+l3)/30,ylength=l2,zlength=(l1+l2+l3)/30,color=yellow], [rod2,'Block',point=MakeTranslations(a2,-l1/2,0,-l3/2),xlength=(l1+l2+l3)/30,ylength=l2,zlength=(l1+l2+l3)/30,color=yellow], [rod2,'Block',point=MakeTranslations(a2,-l1/2,0,l3/2),xlength=(l1+l2+l3)/30,ylength=l2,zlength=(l1+l2+l3)/30,color=yellow], [rod2,'Block',point=MakeTranslations(a2,l1/2,l2/2,0),xlength=(l1+l2+l3)/30,ylength=(l1+l2+l3)/30,zlength=l3,color=yellow], [rod2,'Block',point=MakeTranslations(a2,l1/2,-l2/2,0),xlength=(l1+l2+l3)/30,ylength=(l1+l2+l3)/30,zlength=l3,color=yellow], [rod2,'Block',point=MakeTranslations(a2,-l1/2,-l2/2,0),xlength=(l1+l2+l3)/30,ylength=(l1+l2+l3)/30,zlength=l3,color=yellow], [rod2,'Block',point=MakeTranslations(a2,-l1/2,l2/2,0),xlength=(l1+l2+l3)/30,ylength=(l1+l2+l3)/30,zlength=l3,color=yellow]): >DefineObjects([auxiliary_observer_A1,'Cylinder',orient=MakeRotations(Pi/2,1),length=l2+.1,radius=2*l3/3*radius,color=red]):
>GeometryOutput(main=world,parameters=[l1,l2,l3,radius],states=[q1,q2,q3,q4,q5,q6,theta],anims=[c4=cos(q4),c5=cos(q5),c6=cos(q6),s4=sin(q4),s5=sin(q5),s6=sin(q6)],checktree,checkargs,filename="hinge.geo");
>MotionOutput(ode={q1t=u1,q2t=u2,q3t=u3,q4t=u4,q5t=u5,q6t=u6,thetat=u7},states=[q1,q2,q3,q4,q5,q6,theta],parameters=[l1=2,l2=.25,l3=.05,radius=1.2],anims=[c4=cos(q4),c5=cos(q5),c6=cos(q6),s4=sin(q4),s5=sin(q5),s6=sin(q6)],insignals=[u1=(t&>0)*(t&<1)*cos(6.28*t),u2=(t&>1)*(t&<2)*cos(6.28*t),u3=(t&>2)*(t&<3)*cos(6.28*t),u4=(t&>3)*(t&<4)*cos(6.28*t),u5=(t&>4)*(t&<5)*cos(6.28*t),u6=(t&>5)*(t&<6)*cos(6.28*t),u7=(t&>6)*(t&<8)*cos(6.28*t)+(t&>8)*t],checksings,checkargs,filename="hinge.dyn");
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