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An approach for kinematic synthesis of mechanisms is proposed when the constraints define an algebraic curve. This method first computes a numerical cellular decomposition of the real part of the curve. In such a decomposition, each edge is represented by an interior point and a homotopy that permits tracking along the edge. This numerical representation of each edge is converted to Chebyshev interpolants which facilitate efficient optimization of an analytic or non-analytic function. Illustrative examples along with synthesizing a four-bar linkage are provided which utilize Bertini_real to compute a numerical cellular decomposition and Chebfun to compute Chebyshev interpolants.

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Kinematic Synthesis over Curves Using Cellular Decompositions and Chebyshev Interpolants

  • 会议论文

  • 发表日期：

    2026年

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  • Silviana Amethyst,
  • Jonathan D. Hauenstein,
  • Charles W. Wampler

摘要

An approach for kinematic synthesis of mechanisms is proposed when the constraints define an algebraic curve. This method first computes a numerical cellular decomposition of the real part of the curve. In such a decomposition, each edge is represented by an interior point and a homotopy that permits tracking along the edge. This numerical representation of each edge is converted to Chebyshev interpolants which facilitate efficient optimization of an analytic or non-analytic function. Illustrative examples along with synthesizing a four-bar linkage are provided which utilize Bertini_real to compute a numerical cellular decomposition and Chebfun to compute Chebyshev interpolants.