I've got robotic arm with 6 DoF. I make constrain that x, z carteasian coordinate and orientation is exactly specified. I would like to get joint coordinates which are at cartesian position [x, y_max, z], where y_max is the maximum y cartesian coordinate which is reachable by the end-effector of the robotic arm.
For example: I set x to be 0.5, z to by 1.0 and I want to find joint coordinates that satisfy after forward kinematics that robot's end-effector is at cartesian coordinates [0.5, maximum reachable coordinate, 1.0].
I know that if I know cartesian position and orientation I can find joint coordinates by inverse kinematics and check if the end-effector is at desired coordinateds by forward kinematics, but what if I don't know one of the axis in cartesian and it depends on robot how far it is possible to move? As far as I know, inverse kinematics is possible to solve analyticaly or numericaly, but to solve it I need to know the whole frame of the finish coordinate.
Moreover I would like to have orientation dependent on y coordinate. (for example I would like to guarantee that end-effector is always looking at coordinates [0.5, 0, 0]).