An algorithm for the constant-time solution of systems of geometric
constraint equations is presented in this work. Constraint equations and
their Jacobians may be used in conjunction with other numerical methods
to solve for a variety of kinematics, dynamics, and assembly
optimization problems.  The use of constraint equations for these
purpose is an under-utilized method in this area.  The use of
quaternions for coordinates in these constraint equations is shown to be
a key choice in the optimization problem for avoiding local minima.