Manipulator Dynamics Lagrange approach Newton-Euler approach

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Presentation transcript:

Manipulator Dynamics Lagrange approach Newton-Euler approach Hamiltonian approach

Lagrange dynamics The Lagrangian, “L”, of any system is defined as: (1) where:

Lagrangian Dynamics for 2-Link Manipulator The Lagrangian, “L”, of any system is defined as:

Lagrange dynamics Furthermore, we have:

Lagrange Equation

Two-link manipulator

Kinetic energy of n-1 link

Potential energy of link-1 potential energy of link-1 can be presented as:

kinetic energy of link-2

Lagrangian dynamics of 2-link manipulator (cont)

Lagrangian dynamics of 2-link manipulator Kinetic energy of link – 2 is:

Lagrangian dynamics of 2-link manupulator Potential energy of link 2 is: P2 = - m2gd1C1 – m2gd2C12 where C1 = cos (θ1) C12 = cos(θ1 + θ2)

Total kinetic and potential energy Kinetic energy: K= K1 + K2

Total potential energy Potential energy: P1 + P2

Lagrangian of the system L = K – P

Lagrange dynamics

Lagrange dynamics

Torque T1

Link 2

Torque T2

Torques - interpretation

Torques