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A unified approach to kinematic synthesis of mechanism by adaptive curve fitting

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Abstract

A unified approach to kinematic synthesis of mechanism is presented in this paper. Firstly a new approach to adaptive curve fitting is presented, which leads the normal fitting error to be minimum for a series of given discrete points, including a plane curve fitting, a spherical curve fitting and a ruled surface fitting in terms of invariants of ruled surface. Approximate characteristic points and lines are defined, such as an approximate circle point, an approximate slide point, an approximate spherical cone point and an approximate constant axis with an approximate spherical image cone point and an approximate striction curve. Then, the ruled surface fitting will be converted into a space curve fitting and a spherical curve fitting by differential geometry. Based on these definitions and the adaptive curve fitting approaches, the unified mathematical model is set up for the kinematic synthesis of mechanism from planar, spherical to spatial motion. Finally, a planar mechanism or a spatial mechanism can be synthesized by means of searching for two approximate characteristic points, or a characteristic point and a characteristic line, even two characteristic lines. This puper lays a theoretic base for the existence of the best solution and the convergence of the optimum algorithm.

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Authors and Affiliations

  1. School of Mechanical Engineering, Dalian University of Technology, 116024, Dalian, China

    Wang Delun & Wang Shufen

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  1. Wang Delun
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  2. Wang Shufen
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Correspondence to Wang Delun.

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Wang, D., Wang, S. A unified approach to kinematic synthesis of mechanism by adaptive curve fitting. Sci. China Ser. E-Technol. Sci. 47, 85–96 (2004). https://doi.org/10.1360/02ye0455

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  • DOI: https://doi.org/10.1360/02ye0455

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