17.4 DYNAMICS FOR KINEMATICS CHAINS

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There are a variety of common methods,

- Euler-Lagrange - energy based

- Newton-Euler - D'Alembert's equations

17.4.1 Euler-Lagrange

This method uses a Lagrangian energy operator to calculate torques

For a typical link,

If we have used matrices to formulate the problem, we use the Jacobian to find velocities.

Consider the example below,

17.4.2 Newton-Euler

We can sum forces and moments, and then solve the equations in a given sequence.

These equations can be written in vector form,

To do these calculations start at the base, and calculate the kinematics up to the end of the manipulator (joint positions, velocities and accelerations). Then work back from the end and find forces and moments.