can we have the same TCP position and orientation for multiple configuraiton angles of the robot
The number of DOF of a manipulator tells us if it's possible or not to reach a pose (position + orientation) in the operational space at hand (usually 6-dimensional).
- If we work in a 6D operational space, then we are required to have at least a 6-DOF manipulator to reach a full pose (when this pose is within the allowed range).
- If we deal with a planar manipulator and we are interested in attaining only a target position (i.e. no orientation), then we need a 2-DOF manipulator at least.
- Same as above but now we include the orientation of the gripper; it follows that we need at least a 3-DOF manipulator.
Notice how I've highlighted the term "at least".
On the other hand, nothing is said about how many joint configurations can resolve the single given target pose.
In general, we have many joint configurations! A clear example of that is provided by a 6-DOF manipulator that can easily move all its joints while keeping the position as well as the orientation of the tip fixed. The latter can be achieved by resorting to the so-called null-space projection method.