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Sizing a Serial Chain to Fit a Task Trajectory Using Clifford Algebra Exponentials Pérez Gracia, Alba McCarthy, John Michael Universitat Politècnica de Catalunya. Departament d'Enginyeria Mecànica Universitat Politècnica de Catalunya. CDEI-DM - Centre de Disseny d'Equips Industrials-Dinàmica de Màquines Àrees temàtiques de la UPC::Enginyeria mecànica Mechanical movements Clifford algebra kinematics synthesis Moviments mecànics In this paper we formulate the “generalized inverse kinematics problem” for a spatial serial chain, where the goal is to determine values for structural parameters as well as for the joint parameters. The kinematics equations of the chain are formulated first using matrix exponentials and then cast into a form based on exponentials in a Clifford algebra. These equations contain the coordinates of the joint axes explicitly and have a systematic structure that can be exploited in their solution. As an example we fit a seven degree-of-freedom CCS chain to a 12 position task trajectory. In this problem, we can also specify desired values for the first two joint angles, and compute the structural parameters and the remaining joint angles. Peer Reviewed Postprint (author's final draft) 2005 Conference report Perez Gracia, A.; McCarthy, J. Sizing a Serial Chain to Fit a Task Trajectory Using Clifford Algebra Exponentials. A: IEEE International Conference on Robotics and Automation. "Proceedings of the 2005 IEEE International Conference on Robotics and Automation". 2005, p. 4720-4726. https://hdl.handle.net/2117/363172 eng https://ieeexplore.ieee.org/document/1570847 http://creativecommons.org/licenses/by-nc-nd/3.0/es/ Restricted access - publisher's policy Attribution-NonCommercial-NoDerivs 3.0 Spain 7 p. application/pdf