321 kinematic structure

The inverse kinematics of serial manipulators with six revolute joints, and with three consecutive joints intersecting, can be solved in closed form, i.e. analytically.^[1]^[2] The 321 kinematic structure is a kinematic structure most commercial serial manipulators nowadays have.
The design is an example of a 6R wrist-partitioned manipulator: the three wrist joints intersect, the two shoulder and elbow joints are parallel, the first joint orthogonally intersects the first shoulder joint.
Many other industrial robots, such as for example the PUMA, have a kinematic structure that deviates a little bit from te 321 structure. The offsets move the singular positions of the robot away from places in the workspace where they are likely to cause problems.

References

^ D. L. Pieper. The kinematics of manipulators under computer control. PhD thesis, Stanford University, Department of Mechanical Engineering, 1968.
^ Bruyninckx, Herman, De Schutter, Joris. Introduction to intelligent robotics.

[1] D. L. Pieper. The kinematics of manipulators under computer control. PhD thesis, Stanford University, Department of Mechanical Engineering, 1968.

[2] Bruyninckx, Herman, De Schutter, Joris. Introduction to intelligent robotics.

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