Hierarchical Transformations: 3D Articulated Arm

1. Consider a complex character model with a hierarchical structure. The character has a head, two arms, and two legs, all connected to the main body. If the character performs a complex movement like a cartwheel, how would the hierarchical structure facilitate this animation?
2. In a hierarchical modeling system, how would you implement a scenario where a character's hand needs to remain stationary while the rest of the arm moves?
3. Imagine a scene with a robot arm. The arm has multiple joints, each with its own degree of freedom. How would you use hierarchical modeling to control the movement of the robot arm and ensure that each joint moves correctly in relation to the others?