Reference no: EM131281122
Question
Consider the two-link planar manipulator shown below with link length l1, l2 mass m1, m2 the distance of the center of mass of the links from the joints lc1, lc2 and centroid moment of inertia I1, I2. The coordinates describing the system are q1 , q2 and the respective joint torques τ1, τ2.
1. Derive the equations of motion (q¨1 = f1(q1 , q2 , q.1 q.2), and q¨2 = f2(q1 , q2 , q.1 , q.2 ) ) by hand using NewtonEuler's method.
2. If torsional springs of stiffness k1, k2 are added to the joints, how do the equations get modified?
3. Using the skeleton code provided in myOde.m, solve the dynamic equations from part (1) over 5 seconds. Assume Ic1 = 0.5 Ic2 = 0.5 and all other parameters are 1.0 in their own consistent MKS units. The initial parameters of the systems are:
q1 (0) = Π/3, q2 (0) = Π/4
q.1 (0) = 0 , q.2 (0) = 0
4. Using function getTotalEnergy.m provided, calculate the kinetic, potential, and total energy. Create a plot showing how these energies change during the simulation time, make sure to add a title and label the axes correctly. A common practice to check if the integration was done correctly is to plot the energy of the system. Explain how this information could be used to prove the numerical solution is correct.
Use File testCodeMain.m to test your ODE, but you can change the inputs and outputs of the functions as you see fit.
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