Task Space Description for Robot Arm Activities

What is the task space for a robot arm writing on a blackboard?

a. 2D space

What is the task space for a robot arm twirling a baton?

b. 3D space

Task Space Description:

The task space for a robot arm writing on a blackboard is two-dimensional (2D), as it involves movement along a flat plane. For a robot arm twirling a baton, the task space is three-dimensional (3D), encompassing movement throughout space.

Explanation:

The task space for a robot arm involved in different activities can be described based on the dimensions and the nature of the movement required. For the robot arm writing on a blackboard, the task space is essentially two-dimensional (2D), where the movements are largely confined to a flat plane, akin to the motion of a ball on a pool table. This is because the writing requires movement along the blackboard surface, which has length and height but negligible depth, much like the examples provided by two-dimensional kinematics.

On the other hand, for a robot arm twirling a baton, the task space becomes three-dimensional (3D) because the motion is not restricted to a single plane. The baton can be twirled in ways that encompass a full range of motion in space, similar to motion described by three-dimensional kinematics, such as a car navigating a winding road.

Therefore, the correct answers are (a) 2D space for the robot arm writing on a blackboard and (b) 3D space for the robot arm twirling a baton, aligning with the descriptions of two-dimensional and three-dimensional kinematics, respectively.