Simulation of Deck Crane

Screenshot of simulation of deck crane:







Used the Lagrangian formulation to derive the equation of motion.
The Denavit-Hartenberg convention is used in specifying the kinematics of the crane's links.
Following is the equation of motion of the suspended cable (which is treated as a spherical pendulum).

phidotdot=-(m*thetadot*l^2*sin(2*theta)*phidot
+2*m*ldot*l*sin^2(theta)*phidot
-m*l*sin(theta)*sin(phi)*sxdotdot
+m*l*sin(theta)*cos(phi)*sydotdot
+k*phi
+ _dampingCoeffPhi*phidot)
/(m*l^2*sin^2(theta)+r);


thetadotdot= (-1.*cos(theta)*cos(phi)*sxdotdot
-cos(theta)*sin(phi)*sydotdot
-sin(theta)*szdotdot-g*sin(theta)
-2*thetadot*ldot
+l*sin(theta)*phidot^2*cos(theta)
-_dampingCoeffTheta*thetadot)/l ;



sxdotdot, sydotdot and szdotdot are components of the acceleration of the suspension point, l is the suspended length. The mass of the load is m, r is the inertia of the spin motion of the load, k is the stiffness of the spin motion. Two damping coefficients _dampingCoeffTheta , and _dampingCoeffPhi were added after the equation was derived using the conservative Lagrangian method.

Following is a powerpoint presentation file on the above:
http://www.scribd.com/doc/2519046/APCDemoSlidesFinal2