# Determining the graspable range of a robot arm

I have a 6 DOF robot arm, and I want to do some object grasping experiments. Here, the robot is rigidly mounted to a table, and the object is placed on a different adjacent table. The robot must pick up the object with its gripper parallel to the normal of the object's table, such that it is pointing directly downwards at the point of grasping.

Now, the two tables have adjustable heights. For any given height difference between them. there will be a fixed range of positions over which the robot arm can achieve this perpendicular pose. What I am trying to figure out, is what the optimum relative distance of the tables is such that this range of positions is maximum.

Is there a way to compute this analytically given the robot arm kinematics? Or is there a solution which applies to all robot arms (e.g. it is optimum when the tables are at the same height)?

If it is important, the arm is the Kinova MICO: https://www.youtube.com/watch?v=gUrjtUmivKo.

Thanks!

• can you calculate valid distances of the object to the robot base as a function of relative table height? Commented Aug 5, 2016 at 12:04