Abstract
The operable description of parallel mechanisms is the key to automatic derivation of structural analysis and synthesis. Conformal geometric algebra is introduced to describe robot mechanisms in this paper. A group of basis bivectors {e 23, e 31, e 12, e 1∞, e 2∞, e 3∞} is established to express position and orientation characteristics of the joint axis. The union of each joint’s characteristics of serial mechanisms is defined via outer product operation and the intersection of each limb’s characteristics of parallel mechanisms is defined by shuffle product operation, respectively. In this work, a new algebraic symbol algorithm for end-effectors’ characteristics is proposed and proved validity via two case studies of 3-RRR and 4-URU PMs which is suitable for computer-aided derivation of mechanisms position and orientation characteristics.
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Acknowledgement
The authors would like to acknowledge the financial support of the Natural Science Foundation of China under Grant 51475050 and also thank the reviewers for their suggestions and comments, which have helped to improve the quality of this paper.
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Hang, L., Shen, C., Yang, T. (2016). Structural Analysis of Parallel Mechanisms Using Conformal Geometric Algebra. In: Kubota, N., Kiguchi, K., Liu, H., Obo, T. (eds) Intelligent Robotics and Applications. ICIRA 2016. Lecture Notes in Computer Science(), vol 9834. Springer, Cham. https://doi.org/10.1007/978-3-319-43506-0_14
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