Abstract: A new adjoint approach is developed from differential geometry and is applied to research the kinematic geometry of planar and spatial mechanisms. The constraint curves and the constraint ruled surface of mechanisms are taken as the origin curves and the origin ruled surfaces respetively. A point trajectory and a line trajectory are visualized as an adjoint curve and an adjoint ruled surface, whose invariants are represented by that of the origin curve and surface. The centrodes or axodes are examined as a special case of the adjoint curve or the adjoint surface, whose invariants are exposed in terms of the origin curves and origin surfaces. By taking the centrodes of the axodes and the parameters of the mechanism. The kinematic geometric proparties of a mechanism are revealed in terms of their invariants.

Key words: Adjoint approach, geometry, Kinematic, Mechanisms, Error evaluation, Flatness, Laser ranging, Non-contact measurement