Abstract: An inverse kinematics method of determining joint variables for a manipulator is obtained by forming a model by modifying offset values of a selected arm segments of the manipulator to define a model for which it is possible to derive closed-form inverse kinematics equations for solving the joint variables for said model, developing from said closed-form inverse kinematics equations a system of not more than 3 non-linear equations in not more than 3 unknowns which when solved give an inverse kinematics solution for the model, solving the system of at most 3 non-linear equations to provide the inverse kinematic solution for said manipulator to determine its joint variables.

Abstract: A mirror scanning system comprises a single mirror mounted to rotate on a first axis that is substantially in the plane of the mirror reflecting surface and on a second axis perpendicular to and intersecting the first axis. Both the mirror and the first axis rotate around the second axis. An optical system is directed at a portion of the reflecting surface of the mirror at or adjacent to the intersection of the two axes and has a focal axis substantially aligned with the second axis. By aligning the reflecting surface in a direction so as to maximize a signal emanating from a source and detected at a selected position on a detector forming part of the optical system and measuring the angular displacement of the mirror around each of the first and second axes with the reflecting surface so aligned, the direction of a detected source can be determined.