hw_05 Hanging Sign sol

hw_05 Hanging Sign sol - 42 C 0 A Eltklzk:100r A”...

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Unformatted text preview: 42/ C 0 A % Eltklzk:100r A” ——4 (if; E A “43> 12/ fmhiwm ,g} (“‘93 Li} \H :: : E “:1: 4C: _/ '2»- ?“JO 1; m4v=a -, a a}: Z «(M 2; 5’ a _ L; _. «.mdrms) # 16.80 Him“? (Mm/952m) 5 :4chI 44;) FL 4: (L2: L29) tame wag: LhC) $41.? : me (A ~L29 otrréfxazAleac wow-M) O: : '{H _ LHC: :fl I My: {+00% L» mm) L11}: 4,0ng (4-2) Solution. Sign behavior for Llf= 1.0 and L2f= sqrt(2) just to get started, R un 2, b: 1 .0 xm, ym time Run 2, b=1.0 ' 0.6 0.65 0.7 0.75 0.8 0.85 0.9 0.95 1 xm Thp PD in: at Ym= n 512652 “‘11:; -0 'HR? Thin: in in the directinn exnented (a) This shows that the lengths L1f= 1.2?56 and L2f‘=1.0980 (for A=l, B=0) define an EP at [100,0] Run 2, b=1.0 xm, ym (b) Let the gravity force be zero. Then the EP moves to [ 1.0612, 0.3053, 0.0]. It m, ves to the right and up, as expected with no load force. This result was obtained by simulation. (C) What happens ifthe L2fis 10% short, compared with art (a)? P R un 2, b = 1 .0 rm. ym ' o 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 time At EP xm= 0.8920 and vm=-0.0918. The sign droops and moves toward the wall. as expected xm, state vector: mass velocity components, global variables for convenience and efficiency oi calculation global A, global B, global g, global kl, global Lfll global k2 global LfR, global m, global b .2 “.0; % y offset(above 0} of spring 1 attachment point B: 0.0- y offsetibelow 0) of spring 2 attachment point gravity acceleration % #1: 100.0; % spring 1 stiffness 2 Lf1= A*sgrt( ); % spring 1 free length k2; 100.0; Lf2: A; m= 1.0; % mass b: 1.0; % damping introduced for computational stability % set time vector set initial conditions £5: [0.0:0.01;5.01; x0: [ 0.0: 0.0; A; 0.0 J; % <;_ [t,x] = % generate solution ode23( 'HSegns',ts,xo ]; :,3); % unload results for convenience plot [t,xm,'k',t title ('Run 2, b Xlabe1('time‘}; ylabeli'xm, loqend [ ' xn‘. ' , grid on; ause; ‘Ifiiot(xm,ym}: titloi‘Run 2, o Z.o xlabel['xm'); ylabcli'yn'); grid on; H;lobal A, global B, global g, glooal kl, globe; Lil, global k2, global m, global b % Set up local variables for convenience in coding vx: xii): % Xivelocity of mass Vy= X(2); xm= x(3): % X-position oi mass ym= x(4]; % % Calculate spring lengths from [ xm.ym J L1 sqrt(xm“2+[A-ym)‘2); % spring 1 length L2: sqrt[xm“2+[B+ym)A2}; % Spring 2 length % Calculate spring forces from [ Ll,L2 ] Fl= kl*(ul-Lfl); 52: k2*[42-Lf2); % % Calculate transformation array between [51,F2] and [Fxp,pr] tlx= xm/Ll; t1y= (ym—A)/Ll; t2x= xm/LZ; t2y= (B+ym)/L2; Exp: tlx*F1 +t2x*F2; prr t1y*Fl +L2y*F2; % force on joint P in xidir from springs % force on joint P in y-dir from springs % Set up the input forces Fx= 0.3; % no ex:ernal x :orce Ty: —m*g; % gravity force ucicjtil)= (unflrbkvx —l'xp xdoti2): {J,r)*[-D*vy *ch « Xdot{3)e VY, xdct{4}= vy; t xdot= xdot‘; % return xdot as a column vector % ...
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hw_05 Hanging Sign sol - 42 C 0 A Eltklzk:100r A”...

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