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# Modeling and Simulation of a Four Bar Mechanism and a Crane using ProM - PDF

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### Modeling and Simulation of a Four Bar Mechanism and a Crane using ProM - PDF

1. 1. [Project-4] [Mechanism Studies] Sasi Bhushan Beera #35763829 Srikanth Avala #35762927
3. 3. 0.50 0.50 6.00 Length of the Crank : 6 in Length of the Coupler: 24.7386 in Length of the Follower: 12 in The Crank and the Coupler have to be of negligible mass. So the density is appropriately chosen. The various parameters are tabulated as below: Volume = length * width*thickness + pi * r^2*thickness r: radius of curvature of the ends Link# Length(in) Width(in) Thickness(in) v1 Density Volume Mass Crank 6 1 0.5 0.3925 1.00E-07 3.3925 3.3925E-07 Coupler 24.7386 1 0.5 0.3925 1.00E-07 12.7618 1.27618E-06 Follower 12 1 0.5 0.3925 0.0007324 6.3925 0.004681867 The Four bar mechanism built in pro-E is as shown in the figure below:
4. 4. Four Bar in Pro-E Analysis: The Four bar mechanism is simulated in Pro-E and both kinematic and dynamic analysis is done to measure the angle rates and angular acceleration. The Torque and the reaction forces at the Crank- Ground joint are also measured and are shown in the figures below: Initial Configuration: # Angle(rad) Rate(rad/s) Acceleration(rad.s^2) Crank pi/2 2*pi 0 Follower pi/2 TBD TBD The angular rates , accelerations of other joints and torque and reaction forces at the Crank-ground joint are plotted as shown below:
5. 5. W3 vs time W4 vs time
6. 6. W3dot vs time W4dot vs time
7. 7. Fx Fy
8. 8. Moment Analytical Calculations: Notations: cos(th1) : C1 sin(th1) : S1 cos(th2):C2 sin(th2):S2 cos(th4):C4 sin(th4):S4 Closed loop equations: position level l1*C1+l2*C2 = l0+l3*C4
9. 9. l1*S1+l2*S2 =l3*S4 Differentiating the above set of equations w.r.t time we get equations at velocity level: -l1*S1*w2-l2*S2*w3 = -l3*S4*w4 l1*C1*w2+l2*C2*w3 = l3*C4*w4 Now given w2 we can determine, w3 and w4 at the initial position. Differentiating the above equations w.r.t time we get equations at acceleration level: -l1*S1*α2-l1*C1*(w2^2)-l2*S2* α3-l2*C2*(w3^2) = -l3*S4* α4-l3*C4*(w4^2) l1*C1*α2-l1*S1*(w2^2)+l2*S2* α3-l2*S2*(w3^2) = l3*C4* α4-l3*S4*(w4^2) α3 and α4 can be determined from the above set of equations. Force Calculations: Rocker: F = (I03*w4dot)/(l3*cos(th)) Crank: Rx = -F* cos(th) Ry = -F*sin(th) M = -F*cos(th)*l1 Results: Since pro-E uses relative angles we need to covert them to absolute angles before comparison # Pro-E Analytical Relative Absolute Absolute w3 -360 0 0 w4 180 180 180 α3 282.665 282.665 282.7473 α4 141.354 141.354 141.3717
10. 10. Force Analysis: The hand calculations for the force analysis are submitted in a hand-written format. The results are tabulated as shown below: # Pro-E Analytical Fx -0.0473429 0.0462 Fy -0.012 0.0115 Torque 0.284036 0.2772
11. 11. Part B - The Dutch Crane Introduction: The crane below is a planar four-bar mechanism mounted on a rotating platform. Its critical dimensions are shown in the schematic below in meters. The maximum motion of the crane is given by its driven angle Q which varies from 49 degrees at maximum reach to 132 degrees at minimum reach. Objective The objective here is to render the crane shown above in ProE using reasonable representations for its components and create an appropriate assembly. The then rendered assembly is to be animated using ProE mechanism package. The rendered components: The major components are modeled according to the crane shown in the fig above.
12. 12. The Base: ``
13. 13. The arm: The Rotor:
14. 14. The supporter(long arm)
15. 15. The final rendering of the assembly:
16. 16. Conclusion: Therefore, the four bar mechanism is modeled in Pro-E and kinematic and dynamic analysis is performed to determine the joint rates, accelerations, reaction forces and torques at the joints. And we compared the Pro-E analysis results with the analytical calculations and they agreed with a good degree of precision. The Dutch crane shown is successfully rendered in ProE using idealized models for the components. The dimensions for the components are approximated to the original values shown in the figure. The final rendered assembly is shown above and is animated using ProE mechanism package. The maximum motion of the crane is given by its driven angle Q which varies from 49 degrees at maximum reach to 132 degrees at minimum reach.