TRUE OR FALSE: A finite force can be applied to the end effector that produces no torque at the robot’s joints.

Analysis

To determine whether the statement is true or false, we need to consider the relationship between forces, torques, and the configuration of a robotic arm.

1. Understanding Torque: Torque ($\tau$) is calculated as: $\tau = r \times F$ where $r$ is the position vector (the distance from the joint to the point where the force is applied) and $F$ is the force vector.

2. Conditions for No Torque: For a finite force applied at the end effector to produce no torque at the joints:

   • The force must be applied along the line of the joint's rotational axis.
   • Or, the position vector $r$ at the point of application must be zero (the force is applied directly at the joint).

Conclusion

Given these points, it is possible to apply a finite force at the end effector without producing torque at the joints, provided the conditions mentioned above are met.

Final Answer

TRUE. A finite force can be applied to the end effector that produces no torque at the robot’s joints under specific conditions.