As shown in the animation below, you can experiment with values for the MAMBO parameters and MAMBO state variables to achieve a configuration that approximately satisfies the constraints that
- The magenta-colored spheres representing the instantaneous contact points on the tire and the surface of the plane, respectively, coincide; and
- The tangent plane to the tire at the point of contact agrees with the surface of the plane.
Use the MAMBO toolbox to obtain values for the MAMBO state variables that satisfy the configuration constraints to a higher degree.
In the MAMBO toolbox, type
>const:={seq(FindTranslation(P1,P2) &oo cat(w,k),k=1..3),w3 &oo MakeTranslations(b,-R*(1+1/20*cos(q8))*sin(q7),R*(1+1/20*cos(q8))*cos(q7),0),w3 &oo MakeTranslations(b,-R/20*sin(q8)*cos(q7),-R/20*sin(q8)*sin(q7),R/20*cos(q8))};
>eqs:=evalf(subs(q1=0,q2=0,q4=0.3,q5=0.7,q6=1.7,R=1,const));
>fsolve(eqs,{q3=0.7,q7=3,q8=5.5,q9=.22,q10=-.74});
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