What is the minimum number of DOFs required to reach any position and orientation in 3D space, and why?

• A. Six DOFs (three translational, three rotational).
• B. Three DOFs.
• C. Two DOFs.
• D. Four DOFs.

Answer: (A)

Reaching any position and orientation in 3D space requires six independent parameters: three for where the body is (x, y, z) and three for how it is oriented (rotations about the x, y, and z axes, i.e., roll, pitch, and yaw). This matches the space of rigid-body poses in 3D, SE(3), which is six-dimensional. The translation part moves the point anywhere in 3D, while the rotation part lets you point in any direction and tilt to any angle. With fewer than six degrees of freedom, some combinations of position and orientation can’t be achieved; with six, you can describe every possible pose. Therefore six DOFs is the minimum needed.