We use the recently introduced factorization theory of motion polynomials over the dual quaternions and cubic interpolation on quadrics for the synthesis of closed kinematic loops with six revolute joints that visit four prescribed poses. The resulting 6R linkages are special in the sense that the relative motions of all links are rational. They exhibit certain elegant properties such as symmetry in the rotation angles and, at least in theory, full-cycle mobility. Our synthesis approach admits either no solution or two one-parametric families of solutions. We suggest strategies for picking good solutions from these families. They ensure a fair coupler motion and optimize other linkage characteristics such as total rotation angle or linkage size. A comprehensive synthesis example is provided.
Four-Pose Synthesis of Angle-Symmetric 6R Linkages
Contributed by the Mechanisms and Robotics Committee of ASME for publication in the JOURNAL OF MECHANISMS AND ROBOTICS. Manuscript received September 20, 2013; final manuscript received November 14, 2014; published online March 23, 2015. Assoc. Editor: Andrew P. Murray.
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Hegedüs, G., Schicho, J., and Schröcker, H. (November 1, 2015). "Four-Pose Synthesis of Angle-Symmetric 6R Linkages." ASME. J. Mechanisms Robotics. November 2015; 7(4): 041006. https://doi.org/10.1115/1.4029186
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