Abstract
Mobility analysis determines the number of degree of freedom (DOF) and the motion pattern of a mechanism. Geometric algebra is applied to mobility analysis of two limited-DOF parallel mechanisms (PMs). Based on the outer product in geometric algebra, this method has the advantage in terms of geometric interpretation. It also can simplify the calculation because only addition and multiplication are involved during the whole computation.
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References
Clavel, R.: A fast robot with parallel geometry. In: Proc. Int. Symposium on Industrial Robots (1988)
Wahl, J.: Articulated tool head. Google Patents (2002)
Neumann, K.-E.: Robot. Google Patents (1988)
Hestenes, D.: New foundations for classical mechanics. Springer (1999)
Clifford, W.K.: On the classification of geometric algebras. Mathematical Papers, 397-401 (1882)
Clifford, W.K.: Elements of dynamic: an introduction to the study of motion and rest in solid and fluid bodies. MacMillan and Company (1878)
Clifford, W.K.: On the space-theory of matter. In: Proceedings of the Cambridge Philosophical Society (1876)
Hitzer, E., Helmstetter, J., Abłamowicz, R.: Square roots of–1 in real Clifford algebras. Quaternion and Clifford Fourier Transforms and Wavelets. Springer (2013)
Aristidou, A., Lasenby, J.: Inverse kinematics solutions using conformal geometric algebra. Guide to Geometric Algebra in Practice. Springer (2011)
Aristidou, A., Lasenby, J.: FABRIK: a fast, iterative solver for the inverse kinematics problem. Graphical Models 73, 243–260 (2011)
Zamora, J., Bayro-Corrochano, E.: Inverse kinematics, fixation and grasping using conformal geometric algebra. In: Proceedings of the 2004 IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS 2004). IEEE (2004)
Tanev, T.K.: Singularity analysis of a 4-DOF parallel manipulator using geometric algebra. In: Advances in Robot Kinematics. Springer (2006)
Tanev, T.K.: Geometric algebra approach to singularity of parallel manipulators with limited mobility. In: Advances in Robot Kinematics: Analysis and Design. Springer (2008)
Li, Q.C., Chai, X.X.: Mobility analysis of limited-DOF parallel mechanisms in the framework of geometric algebra. Submitted to the Journal of Mechanisms and Robotics
Hildenbrand, D.: Foundations of Geometric Algebra Computing. Springer (2012)
Vince, J. A.: Geometric algebra for computer graphics. Springer (2008)
De Sabbata, V., Datta, B.K.: Geometric algebra and applications to physics. CRC Press (2006)
Dorst, L., Fontijne, D., Mann, S.: Geometric algebra for computer science (revised edition): An object-oriented approach to geometry. Morgan Kaufmann (2009)
Lipkin, H., Duffy, J.: The elliptic polarity of screws. Journal of Mechanical Design 107, 377–386 (1985)
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Chai, X., Li, Q. (2014). Mobility Analysis of Two Limited-DOF Parallel Mechanisms Using Geometric Algebra. In: Zhang, X., Liu, H., Chen, Z., Wang, N. (eds) Intelligent Robotics and Applications. ICIRA 2014. Lecture Notes in Computer Science(), vol 8917. Springer, Cham. https://doi.org/10.1007/978-3-319-13966-1_2
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DOI: https://doi.org/10.1007/978-3-319-13966-1_2
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-13965-4
Online ISBN: 978-3-319-13966-1
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