Kinematic Analysis for the Spatial Interlocking 3-UU Mechanism With the Wide Range of Motion

• Published in: IEEE robotics and automation letters Vol. 9; no. 4; pp. 3926 - 3931
• Main Authors: Lang, Guodong, Gao, Yongsheng, Luo, Zhewen, Liang, Guanlin, Zhu, Yanhe, Zhao, Jie
• Format: Journal Article
• Language: English
• Published: Piscataway IEEE 01.04.2024; The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
• Subjects: biologically-inspired robots; compliant joints and mechanisms; Jacobian matrices; Kinematics; lie group; Lie groups; Locking; Motors; parallel robots; Quaternions; Radar tracking; Range of motion; Read only memory; Robotics; Robots
• ISSN: 2377-3766; 2377-3766
• DOI: 10.1109/LRA.2024.3372439

Mechanisms that balance wide range of motion(ROM) with increased stiffness are gradually gaining attention in robotic applications. This letter proposed kinematic methods for the spatial interlocking 3-UU mechanism based on Lie Group, which consists of a fixed base and a moving platform connected by three serial limbs. A previous mathematical mobility analysis confirms that the mechanism has 0 degrees of freedom (DoFs), and the prototypes demonstrate unexpected large platform motions. Since the 3-UU mechanism theoretically has zero DoFs, existing serial and parallel kinematic methods cannot determine its motion. This study addresses this seeming contradiction. We propose a kinematic method based on the renowned Baker-Campbell-Hausdorff formula in Lie Group. Upon optimization, the positional error is limited to a maximum of 0.71 mm at a 250 mm length within an actuated joint motion range of 30<inline-formula><tex-math notation="LaTeX">^{\circ }</tex-math></inline-formula> (-15<inline-formula><tex-math notation="LaTeX">^{\circ }</tex-math></inline-formula> to 15<inline-formula><tex-math notation="LaTeX">^{\circ }</tex-math></inline-formula>). This result represents a significant step in addressing the unexplored domain of the kinematic method of 3-UU mechanisms and promoting the widespread application of the mechanism.