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Open Access Publications from the University of California

Scholarly Works (4 results)

  • Thesis
  • Peer Reviewed
UC Irvine Electronic Theses and Dissertations (2014)

This dissertation presents research into the automation of the configuration analysis of eight-bar linkages based on the known 16 linkage topologies. The eight-bar linkage topologies do not distinguish a ground link or an input link, and this research shows that the selection of a ground link yields 71 unique mechanisms. In addition, the selection of a driving link attached to ground results in 153 eight-bar linkages with distinct sets of loop equations. The research automates the configuration analysis process and has been demonstrated for four-bar and six-bar linkages as well as eight-bar linkages. A check of the process includes example 10-bar linkages.

The automation of linkage analysis begins with an adjacency matrix, which defines how the joints connect the links known as the topology of the linkage. The ground link and driving link are selected by the designer, and the automated analysis process determines the smallest set of independent loops. A naming convention is used to automate the definition of link features, dimensions, and joint angles, which yields a text version of the loop equations for the linkage. These loop equations are solved using the Dixon determinant to find the configuration of the linkage for each value of the driving link angle. This formulation also yields the Jacobian of the loop equations, and factors its determinant which is used to find the singularities of the linkage.

The contribution of this research is an automated analysis of eight-bar linkages that applies to four-bar and six-bar linkages, and has been useful in the analysis of 10-bar linkages. This approach has provided a new classification of the 153 eight-bar linkages by family, link assortment, topology, mechanism, and linkage. The automation process can formulate the loop equations and Jacobian conditions for all 153 cases, as well as for all four-bar and six-bar cases.

Automated configuration analysis for eight-bar linkages provides an important tool for evaluating the range of movement of linkages obtained in mechanism synthesis algorithms, allowing identification of linkages that achieve a required task.

    Cover page: Automated Configuration Analysis of Planar Eight-Bar Linkages
    • Article
    • Peer Reviewed
    UC Irvine Previously Published Works (2017)
    A cycle basis in an undirected graph is a minimal set of simple cycles whose symmetric differences include all Eulerian subgraphs of the given graph. We define a rooted cycle basis to be a cycle basis in which all cycles contain a specified root edge, and we investigate the algorithmic problem of constructing rooted cycle bases. We show that a given graph has a rooted cycle basis if and only if the root edge belongs to its 2-core and the 2-core is 2-vertex-connected, and that constructing such a basis can be performed efficiently. We show that in an unweighted or positively weighted graph, it is possible to find the minimum weight rooted cycle basis in polynomial time. Additionally, we show that it is NP-complete to find a fundamental rooted cycle basis (a rooted cycle basis in which each cycle is formed by combining paths in a fixed spanning tree with a single additional edge) but that the problem can be solved by a fixed-parameter-tractable algorithm when parameterized by clique-width.
      • Article
      • Peer Reviewed
      UC Irvine Previously Published Works (2015)
      In this paper we present an algorithm that automatically creates the linkage loop equations for planar 1-DoF linkages of any topology with rotating joints, demonstrated up to 8-bars. The algorithm derives the linkage loop equations from the linkage graph by establishing a cycle basis through a single common edge. Divergent and convergent loops are identified and used to establish the fixed angles of the ternary and higher links. Results demonstrate the automated generation of the linkage loop equations for the five distinct 6-bar mechanisms, Watt I-II and Stephenson I-III, as well as the seventy one distinct 8-bar mechanisms. The resulting loop equations enable the automatic derivation of the Dixon determinant for linkage kinematic analysis of the position of every possible assembly configuration. The loop equations also enable the automatic derivation of the Jacobian for singularity evaluation and tracking of a particular assembly configuration over the desired range of input angles. The methodology provides the foundation for the automated configuration analysis of every topology and every assembly configuration of 1-DoF linkages with rotating joints up to 8-bar. The methodology also provides a foundation for automated configuration analysis of 10-bar and higher linkages.
        Cover page: Automated Generation of Linkage Loop Equations for Planar One Degree-of-Freedom Linkages, Demonstrated up to 8-Bar
        • Article
        • Peer Reviewed
        UC Irvine Previously Published Works (2014)
        In this paper, we present an algorithm that automatically creates the linkage loop equations for planar one degree of freedom, 1DOF, linkages of any topology with revolute joints, demonstrated up to 8 bar. The algorithm derives the linkage loop equations from the linkage adjacency graph by establishing a rooted cycle basis through a single common edge. Divergent and convergent loops are identified and used to establish the fixed angles of the ternary and higher links. Results demonstrate the automated generation of the linkage loop equations for the nine unique 6-bar linkages with ground-connected inputs that can be constructed from the five distinct 6-bar mechanisms, Watt I-II and Stephenson I-III. Results also automatically produced the loop equations for all 153 unique linkages with a ground-connected input that can be constructed from the 71 distinct 8-bar mechanisms. The resulting loop equations enable the automatic derivation of the Dixon determinant for linkage kinematic analysis of the position of every possible assembly configuration. The loop equations also enable the automatic derivation of the Jacobian for singularity evaluation and tracking of a particular assembly configuration over the desired range of input angles. The methodology provides the foundation for the automated configuration analysis of every topology and every assembly configuration of 1DOF linkages with revolute joints up to 8 bar. The methodology also provides a foundation for automated configuration analysis of 10-bar and higher linkages.
          Cover page: AUTOMATED GENERATION OF LINKAGE LOOP EQUATIONS FOR PLANAR 1-DOF LINKAGES, DEMONSTRATED UP TO 8-BAR
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