Type Synthesis of Parallel Tracking Mechanism With Varied Axes by Modeling Its Finite Motions Algebraically

Abstract

Parallel tracking mechanism with varied axes has great potential in actuating antenna to track moving targets. Due to varied rotational axes, its finite motions have not been modeled algebraically. This makes its type synthesis remain a great challenge. Considering these issues, this paper proposes a conformal geometric algebra (CGA) based approach to model its finite motions in an algebraic manner and parametrically generate topological structures of available open-loop limbs. Finite motions of rigid body, articulated joints, and open-loop limbs are formulated by outer product of CGA. Then, finite motions of parallel tracking mechanism with varied axes are modeled algebraically by two independent rotations and four dependent motions with the assistance of kinematic analysis. Afterward, available four degrees-of-freedom (4-DoF) open-loop limbs are generated by using revolute joints to realize dependent motions, and available five degrees-of-freedom (5-DoF) open-loop limbs are obtained by adding one finite rotation to the generated open-loop limbs. Finally, assembly principles in terms of minimal number and combinations of available open-loop limbs are defined. Typical topological structures are synthesized and illustrated.