10.7.1.1. Newton-Raphson Method

Try these first

1. 1.

   What is the first step in using the Newton-Raphson Method?

   Hint

   Consider what might happen if you guess too far from the solution.

2. 2.

   Define the Jacobian matrix.

   Hint

   Think about its role in motion analysis.

3. 3.

   What does the Newton-Raphson Method help solve?

   • Inverse Kinematics
   • Forward Kinematics
   • Both

   Hint

   Remember the primary aim of IK.

4. 4.

   True or False: The Jacobian matrix must always be square for the Newton-Raphson Method to work.

   • True
   • False

   Hint

   Consider how robots can have more joints than needed.

5. 5.

   A robotic arm is attempting to reach a position in 3D space defined by given coordinates using the Newton-Raphson Method. Describe how you would calculate the necessary joint parameters.

   Hint

   Start by breaking down the coordinate dimensions.

6. 6.

   You are using the Newton-Raphson Method but encounter a singularity. What steps would you take to address this issue?

   Hint

   What are some adjustments you can make to move away from singularity?