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Methods to derive Dynamical equations: |
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Formulation using Lagrange equation
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Newton's method
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Lagrange Method:- |
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Features: |
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This Method is based on energy. |
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Equations are obtained without considering the internal reaction forces. |
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It is ideal for more complex robotic manipulator configurations. e.g. Complex 3D robot, flexible link robot
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It is better than Newton's method for robotic applications. |
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It is based on differentiation of energy terms with respect to the systems variables & time. In this method we have to form the Lagrangian of the system, which is the difference of kinetic & potential energy of the system. |
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L = K.E.- P.E.
L= Lagrangian , K.E.= Kinetic Energy, P.E.= Potential Energy.
 = external force or torque applied to the system at joint i to drive link i in direction of generalised co-ordinate q i .
q i =generalised co-ordinate which may be joint angle  for revolute joint or offset distance d i
(Please refer D-H representation.) |
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Now we will apply this method to simple systems like spring-mass system. |
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Figure 31.5 Spring- mass system |
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Contd... |
