What is the minimum number of degrees of freedom that a robot needs to have in order to locate its end effectors at an arbitrary point with an arbitrary orientation in space?

Concept:

Degrees of freedom (DOF):

It is defined here as modes in which a mechanical device or system can move. The total number of degrees of freedom is equal to the number of independent displacements or type of motion.

Explanation:

A machine may operate in two or three dimensions but have more than three degrees of freedom. The term is widely used to define the motion capabilities of robots.

Now, a robot arm is built to work as a human arm. And the motion is as follows:

• Shoulder motion can take place as pitch (up and down) or yaw (left and right).
• Elbow motion can occur only as pitch.
• Wrist motion can occur as pitch or yaw.
• Rotation (roll) may also be possible for the wrist and shoulder.

Hence the robot is having 6-7 DOF to perform arbitrary tasks that include both arm and wrist movements.

But in this question, only the location of end effectors is asked hence only 6 DOF robot arm required in order to locate its end effectors at an arbitrary point with arbitrary orientation in space.