11.3.2. Application to Robotics

Try these first

1. 1.

   What is the Lagrangian in robotics?

   Hint

   Think about how energy is stored and used in a system.

2. 2.

   Define Degrees of Freedom in the context of robotics.

   Hint

   Consider how joints function in motion.

3. 3.

   What does the Lagrangian represent in robotics?

   • The total mass
   • The difference between kinetic and potential energy
   • The torque applied

   Hint

   Think about how energy influences motion.

4. 4.

   True or False: The Euler-Lagrange equation is unnecessary for deriving motion equations in robotics.

   • True
   • False

   Hint

   Consider the role of this equation in dynamics.

5. 5.

   You are given a 3-DOF robotic manipulator. Derive its equations of motion using Lagrangian mechanics. Show all workings.

   Hint

   Don't forget to express energies based on the robot's geometry and constraints.

6. 6.

   Discuss how dynamic characteristics such as mass or inertia affect control strategies in robotic systems.

   Hint

   Consider scenarios of unexpected load changes.