For a serial manipulator, what is the primary reason that the inverse kinematics problem often yields multiple solutions for a given end-effector pose?
Question 2
Consider a 2-link planar robotic arm with link lengths $L_1$ and $L_2$. The first joint angle $\theta_1$ is measured from the positive x-axis, and the second joint angle $\theta_2$ is measured relative to the first link. If the end-effector is at position $(x, y)$, which of the following equations is a crucial step in solving the inverse kinematics problem using the geometric approach to find $\theta_2$?
Question 3
In the context of homogeneous transformations, what is the primary function of the $4 \times 4$ matrix?
Question 4
When comparing serial manipulators and parallel manipulators, which statement accurately describes a key difference in their kinematic structure?
Question 5
For a 6R spatial robot, why is the inverse kinematics solution often more challenging to obtain in a closed form compared to a numerical solution?
