# Kinematic decoupling

Is kinematic decoupling of a 5DOF revolute serial manipulator also valid? The three last joints is a spherical joint. Most literatures only talks about decoupling of 6DOF manipulators.

Thanks in advance, Oswald

UPDATE Based on the comment below that the answer is not correct:

Kinematic decoupling divides the inverse kinematics problem into two parts. Coordinates of the wrist center point are calculated and based on those all the joint angles behing the wrist center point have to be determined. If this is possible, kinematic decoupling can be applied in you case. In other words if you can calculate a number of coordinates of the wrist center point that fully determines all joint angles behind your wrist center point than ... there you have it... kinematic decoupling works for you...

Yes, kinematic decoupling will work under 1 condition. You have to be able to determine the XYZ coordinates of your wrist center point (where the wrist axes intersect eachother) from the desired end effector coordinates. If the IK is solvable or not for the given input (i.e. the pose can be reached) is not a question of the kinematic decoupling but a question of the inverse kinematics

I may have been to fast in assuming XYZ, other coordiantes might be OK, depending on how many joints are there behind the wrist, XY could be enough.

If you have 5 DOF and have the desired TCP coordinates (X, Y, A, B, C) you cannot calculate XYZ of the wrist center point, but not calcualting XYZ may be ok, if the coordinates you can calculate are enough to determine all joint angels before the wrist center point., So if you have X and Y of the wrist center point, and 2 joint before the wirst center point, if the X and Y coordaintes fully determine the q1 and q2 angles, kinematic decoupling can be used to write the IK equations.

• Thank you very much for your answer, Brian! and u too 50k4 Nov 17, 2015 at 23:57
• Note that this answer isn't really correct! You can always "determine the XYZ coordinates of your wrist centre", why would that only be possible for manipulators that can be decoupled? Nov 18, 2015 at 0:20
• Not the best wording, I will correct. If the controlled 5 end effectror coordinates do not include all 3 translations (e.g. You want to control X Y A B C, and you do not control Z, it just results from all the others) you will not be able to calculate the XYZ coordinates of your wrist center point. Aditionally the wrist center poin has to exist in order to apply the kinematic decoupling.
– 50k4
Nov 18, 2015 at 6:20
• @Oswaldfig No problem
– 50k4
Nov 18, 2015 at 8:04

Kinematic decoupling really depends on the configuration of your particular manipulator. When you decouple the wrist, it is typically so that you can take any given end-effector pose and determine the required wrist configuration separately before determining the required arm configuration that puts the wrist-connecting joint at the required location.

Typically, the wrist needs to be able to provide the 3 DOF necessary to achieve any orientation for this to be possible. The position of the innermost wrist joint itself is then the desired position for the end of the rest of the manipulator (3 or 4 other DOF). If your wrist provides 3 DOF with a spherical configuration as you mention, then it meets this requirement.

However, if you only have 5 DOF then that means you are underactuated for full 6 DOF end-effector space -- you could come up with an end-effector pose that is impossible to achieve. On the other hand, if you are constraining yourself to work with end-effector poses that you know are possible, then decoupling the wrist will work.

Decoupling the wrist just makes it easier to analyze the inverse kinematics since you can solve for the wrist joint angles separately. In general, the technique could be applied to a wrist that is constrained to planar motion or pan-tilt type rotation only, as long as the desired end-effector pose is achievable.