A robot with 6 joints has how many DOF?

• A. 4
• B. 5
• C. 6
• D. 7

Answer: (C)

Degrees of freedom tells you how many independent motions you can have in a system. In 3D space, a rigid body needs six independent parameters to describe its pose: three translations (x, y, z) and three rotations (roll, pitch, yaw). In a typical robot arm, each joint that moves in one independent way adds one DOF. So a serial chain with six joints that each provide one motion gives six independent motions, meaning the end effector can reach any position and orientation in space. Therefore, six joints yield six DOF. If joints were constrained or shared motion, the DOF would change, but with six one-DOF joints, the six DOF result holds.