Ref: Computational Dynamics, A. Shabana, John & Wiley Consider a following dynamic 4 bar linkage system shown below. ➤ X
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- Ref Computational Dynamics A Shabana John Wiley Consider A Following Dynamic 4 Bar Linkage System Shown Below X 1 (90.83 KiB) Viewed 40 times
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multipliers and define the matrix/vector components explicitly.
2. Derive the following embedded formulation using the
independent system DOF only.
4. Using the augmented formulation from Problem 1 and
system parameters from Problem 3, compute 𝜃 2 , 𝜃̇2 , 𝜃̈2 with your
own code. Any time integrators (Euler, RK4, etc) and any computer
languages(MATLAB, C, Python, etc) can be used.
5. Using the embedded 𝜃̈1 from Problem 2 and system
parameters from Problem 3, compute 𝜃 2 , 𝜃̇2 , 𝜃̈2 with your own
code. Any time integrators (Euler, RK4, etc) and any computer
languages(MATLAB, C, Python, etc) can be used.
Ref: Computational Dynamics, A. Shabana, John & Wiley Consider a following dynamic 4 bar linkage system shown below. ➤ X, Y is the global coordinate. ¹ is the independent DOF of this system. ➤ Origins of local coordinates are placed on each body's center of mass. External torque M¹ is applied at the center of mass of the Body 1. > ➤ Length of each OA, AB, BC, OC is expressed as 1¹, 1², 1³, 14 respectively. y² B X² A Y¹ X¹ Y 77777 M¹ X X³ Y³
1. Derive the following augmented formulation using the Lagrange multipliers and define the matrix/vector components explicitly. [M C 490-6 = 2. Derive the following embedded formulation using the independent system DOF only. Prove your result by BC = 0. M₁ä = Qu M₁ = BIMB₁, ä, = [0¹], Q₁ = BQe - BMY
4. Using the augmented formulation from Problem 1 and system parameters from Problem 3, compute 0², 8²,0² with your own code. Any time integrators (Euler, RK4, etc) and any computer languages(MATLAB, C, Python, etc) can be used. Submit the source code with explanation. Tip 1. Using state space vector, convert the 2nd order ODE to 1st order ODE. Tip 2. Refer to the example code of TA lecture 2. 5. [Bonus point] Using the embedded ¹ from Problem 2 and system parameters from Problem 3, compute 0², ², ² with your own code. Any time integrators (Euler, RK4, etc) and any computer languages(MATLAB, C, Python, etc) can be used. Submit the source code with explanation. Tip 1. Use state vector Y = [0¹, 0², 0³] for numerical integration. Tip 2. Symbolic mathematics package in MATLAB or Python(SymPy) can be useful. Tip 3. Plot of 0² is shown in Fig. 1. 02 100 Python-AugForm Python-EmbedForm 80 RecurDyn 60- 40 20 0.05 0.10 0.15 0.20 0.25 Time (sec) Fig. 1 Plot of 02 in t = [0,0.3] sec. Degree 0.00