A really important consideration with any robot is the set of all possible points that it can reach. And we refer to this volume as the workspace of the robot. For most industrial robot arms in the data sheet that comes with the robot, you could find the diagram that looks something like this. It is a plain view and side elevation view of the robot.
And what you can see here marked in blue is the reachable volume of the robot. We can see that this volume around the body of the robot where it cannot reach either. And this is due to mechanical limits on the range of motion of particular joints or it’s an artifact of the robot control software to prevent parts of the arm intersecting or colliding with other parts of the robot's arm or its base.
The workspace of a robot arm is the set of all positions that it can reach. This depends on a number of factors including the dimensions of the arm.
This content assumes high school level mathematics and requires an understanding of undergraduate-level mathematics; for example, linear algebra - matrices, vectors, complex numbers, vector calculus and MATLAB programming.