Analysis of Serial Mechanism Synthesis with Fewer Degrees of Freedom from A Geometric Point of View

• Published in: IEEE robotics and automation letters Vol. 8; no. 9; pp. 1 - 8
• Main Authors: Xia, Yimin, He, Yuanfu, Yang, Mei, Lin, Laikuang
• Format: Journal Article
• Language: English
• Published: Piscataway IEEE 01.09.2023; The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
• Subjects: Actuators; Algebra; Conformal geometric algebra; Degrees of freedom; Design optimization; Fewer degrees of freedom; Geometry; Joint axis; Kinematics; Layout; Mathematical analysis; Planes; Serial mechanism synthesis; Software; Spatial layout; Synthesis; Task analysis; Topology; Transformations (mathematics)
• ISSN: 2377-3766; 2377-3766
• DOI: 10.1109/LRA.2023.3296253

In order to explain the synthesis process of the serial mechanism in a concise and intuitive geometric perspective, this paper introduces conformal geometric algebra, an effective geometric representation and computational mathematical tool, to describe the actuator poses and joint axes. The actuator pose is represented as three characteristic planes, and the three planes are sequentially overlapped with the corresponding planes of the desired pose to realize the pose transformation requirement. In the process of plane coincidence transformation, the outer product operation of conformal geometric algebra is used to construct the joint axes of the mechanism, and this process can visualize the whole process of mechanism design. Then, the influence of the revolute joint position on the actuator transformation is analyzed, and the rational layout of the revolute joints is used to satisfy the displacement demand of the mechanism instead of the prismatic joints, so as to achieve the mechanism's fewer degrees of freedom optimized design. Finally, the 2R1T and 2R mechanisms are designed according to the set demand of any two poses, and the correctness of the proposed method is verified by using the prototype experiment.