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We clearly see that to use Lagrange method to get dynamical equations for a robotic manipulator first we need to get expression for K.E. & P.E. of Robot manipulator. |
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To get the enrgy we need to know linear velocity of c.g. & angular velocity of each link of Robotic manipulator. we have seen in the modules Kinematics of Robot how to get these velocities expressed in the global co-ordinate reference frame. Explained below is general preocedure to be followed to carry out Lagrange formulation for a Robotic manipulator. |
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Following that we will see use of Lagrange method to obtain equations of dynamics for 2-R manipulator. |
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General procedure for formulation of robot dynamics |
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STEP 1 |
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Perform kinematic analysis to. find out velocities of c.g.'s of robot links. |
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STEP 2 |
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Find the kinetic energy |
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Note Ii is in the link
reference frame
&  |
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STEP 3 |
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Now we will express K.E. as  so that we will get D(q) matrix. Refer kinematic analysis modules for details.
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STEP 4 |
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The Potential energy is  where g = gravity vector in base coordinate system. |
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STEP 5 |
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Now we will apply Lagrange equation (simplified version) to get the robot equation. |
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Note that generalized force may contain damping terms. |
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The equation is 2nd order ordinary differential equation in general nonlinear
. It can be solved for q's, given the torques applied. Its numerical solution can be found out by using MATLAB. |
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