Joint constraints

Joint constraints are rotational constraints on the joints of an artificial system.{{Cite web|url=https://nphysics.org/joint_constraints_and_multibodies/|archive-url=https://web.archive.org/web/20180807150816/http://nphysics.org/joint_constraints_and_multibodies/|url-status=usurped|archive-date=August 7, 2018|access-date=2020-06-08|website=nphysics.org|title=Joint constraints and multibodies}} They are used in an inverse kinematics chain, in fields including 3D animation or robotics.{{Cite book|last1=Knoop|first1=S.|last2=Vacek|first2=S.|last3=Dillmann|first3=R.|title=5th IEEE-RAS International Conference on Humanoid Robots, 2005 |chapter=Modeling joint constraints for an articulated 3D human body model with artificial correspondences in ICP |date=December 2005|chapter-url=https://ieeexplore.ieee.org/document/1573548|pages=74–79|doi=10.1109/ICHR.2005.1573548|isbn=0-7803-9320-1|s2cid=15067294 }} Joint constraints can be implemented in a number of ways, but the most common method is to limit rotation about the X, Y and Z axis independently. An elbow, for instance, could be represented by limiting rotation on X and Z axis to 0 degrees, and constraining the Y-axis rotation to 130 degrees.

To simulate joint constraints more accurately, dot-products can be used with an independent axis to repulse the child bones orientation from the unreachable axis. Limiting the orientation of the child bone to a border of vectors tangent to the surface of the joint, repulsing the child bone away from the border, can also be useful in the precise restriction of shoulder movement.