What does a continuous path in Cartesian space imply for the end effector?

• A. The end effector follows a smooth trajectory through space.
• B. The robot only moves joints in place.
• C. The path avoids obstacles without planning speed.
• D. The path is defined purely in joint space.

Answer: (A)

A continuous path in Cartesian space means the end effector’s position in the fixed world frame changes smoothly over time, tracing a curve in 3D space without any jumps. This describes the actual spatial motion of the hand or gripper, independent of the specific joint motions that achieve it. Since Cartesian space uses x, y, z (and possibly orientation) to define position, a single spatial path can be realized by different joint configurations, but the motion itself remains a smooth progression through space. This is why the end effector follows a smooth trajectory through space.

The other ideas don’t fit because moving joints in place doesn’t produce motion through space, a Cartesian path doesn’t automatically include speed planning or obstacle avoidance, and saying the path is defined purely in joint space contradicts the notion of a Cartesian spatial trajectory.