The use of the image space of planar displacements for planar motion approximation is a well studied subject. While the constraint manifolds associated with planar four-bar linkages are algebraic, geometric (or normal) distances have been used as default metric for nonlinear least squares fitting of these algebraic manifolds. This paper presents a new formulation for the manifold fitting problem using algebraic distance and shows that the problem can be solved by fitting a pencil of quadrics with linear coefficients to a set of image points of a given set of displacements. This linear formulation leads to a simple and fast algorithm for kinematic synthesis in the image space.
A Novel Approach to Algebraic Fitting of a Pencil of Quadrics for Planar 4R Motion Synthesis
Department of Mechanical Engineering,
Stony Brook University,
Contributed by the Computers and Information Division of ASME for publication in the JOURNAL OF Computing and Information Science in Engineering. Manuscript received March 21, 2012; final manuscript received July 28, 2012; published online September 18, 2012. Assoc. Editor: Bahram Ravani.
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Ge, Q. J., Zhao, P., Purwar, A., and Li, X. (September 18, 2012). "A Novel Approach to Algebraic Fitting of a Pencil of Quadrics for Planar 4R Motion Synthesis." ASME. J. Comput. Inf. Sci. Eng. December 2012; 12(4): 041003. https://doi.org/10.1115/1.4007447
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