Final answer:
The task space for a robot arm writing on a blackboard is a two-dimensional plane corresponding to the blackboard's surface, requiring control over movement and pressure. The task space for a robot arm twirling a baton is three-dimensional, requiring the ability to manipulate the baton with rotational movements and change its orientation.
Step-by-step explanation:
Task Space for a Robot Arm
The task space for a robot arm can be described based on the specific activities it is designed to perform. For part (a), the task space for a robot arm writing on a blackboard would involve a flat, two-dimensional plane that corresponds to the surface of the blackboard. The robot arm would need to have sufficient degrees of freedom to move across the blackboard's surface to write characters and symbols as required. It must also control the pressure applied to the writing instrument to ensure clear and consistent writing without damaging the blackboard.
For part (b), the task space for a robot arm twirling a baton is more complex, as it involves a three-dimensional space where the baton can be manipulated along different axes. This task would require the robot arm to execute smooth, circular, and rotational movements to twirl the baton efficiently. The task space would need to account for the length of the baton, the space needed to rotate it, and the capability to change the baton's orientation while in motion.